What is the difference between a hybrid vehicle and a plug-in hybrid vehicle? And why are plug-in hybrid vehicles better than regular hybrid vehicles, even as good as EVs?
There are even more categories of hybrid vehicles: micro hybrid, mild hybrid, full hybrid, plug-in hybrid.
A micro hybrid has slightly beefed up enhanced flooded lead-acid battery, a starter motor that tolerates frequent use and intelligent charging systems. What they essentially do is that while you drive, the battery is left slightly below full charge. Then when you engine brake, the intelligent charging system realizes now may be a good point to rapidly charge the battery, and the battery is charged very rapidly with full current, to maximize the amount of energy regenerated and minimize need for braking. When you stop at a stoplight, the engine is stopped too. When you want to continue driving again, the engine is rapidly restarted with the starter motor that withstands more frequent use. Then when you drive, initially the charger is providing zero current and the battery is slightly discharged to make it slightly below full charge. Then when the battery is at a certain state of charge, the charging system activates again to maintain this state of charge that allows rapid recharging when engine braking. The benefit here is that engine idling doesn't waste fuel, and part of the electrical load of the car is provided by rapidly charging the battery when engine-braking and then operating on the battery. Therefore, fuel use is slightly reduced.
Mild hybrids typically have heavierweight systems such as 48-volt battery and an integrated starter-generator. Then can provide additional torque to the engine using the 48-volt battery and the integrated starter-generator in the starter (motor) mode. They may have the ability to entirely stop the engine when coasting to a stop, freewheeling. However, none of these vehicles allow driving only on battery power. The battery only slightly provides boost to torque during acceleration. This allows the engine to be slightly smaller. A smaller engine is more fuel efficient.
A regular good full hybrid uses a clever arrangement with an electric continuously variable transmission that has a planetary gearset, two motor-generators in the transmission, and high-voltage inverters to control the motor-generators. There is no ordinary alternator, and no starter motor. The 12-volt battery only boots up the computers. The 12-volt battery is charged from the high-voltage system using a DC-DC converter, and the high-voltage system is kept charged with the motor-generators in generator mode. Because there is no starter motor, the 12-volt battery can't be used to start the engine. Instead, the high-voltage battery and motor-generators in motor mode start the engine. The high-voltage battery is isolated from the car electrical systems by a relay if the car is turned off. The high-voltage battery is typically 200-300 volts 1-4 kWh, and it is shallow cycled. This means that even if you might have 1.6 kWh battery, only some 0.4 kWh of it is actually utilized. By maintaining the battery at the very center of its state of charge, never empty, never full, you can get hundreds of thousands of cycles from the high-voltage battery. The air conditioning compressor is typically electric (allowing air conditioning when engine is stopped), and there is usually at least one electric water pump (allowing fully providing engine heat to heater core when engine is stopped, but eventually the heat is exhausted and engine needs to be turned back on). The transmission, being a planetary gearset, has only one gear but three shafts. It is cleverly used as an electric continuously variable transmission by controlling the motor-generators independently. This allows a transmission that is cheaper than a manual transmission, that has no wearable clutch, and that essentially works like an automatic continuously variable transmission with no wearable belts.
Typically, a full hybrid can drive only 1-5 kilometers on battery charge. The purpose of the battery is not to drive long distances on battery only, but rather to allow a smaller more efficient Atkinson cycle engine (that would be terribly non-torquey on a standard car) to work well, and to allow regenerative braking. Usually regenerative brakes are operated by the brake pedal. If driving down a mountain road, once the battery is full, the car automatically turns on the engine to provide braking by the engine and not overheating the brakes. If driving a regular road, once the battery is full, it transparently changes to disc brakes. The battery may not be usually charged. Even if you could charge it, it would provide so little charge there's no point in charging. There may be strict restrictions on the maximum electric-only speed: between speeds of 50 km/h and 80 km/h there is usually a point where electric-only driving becomes impossible. Also, while the motors in the eCVT transmission allow high-power operation, the battery is usually so small you may not be able to extract more than 20-30 kilowatts out of it. Nickel metal hydride batteries are surprisingly common, but lithium ion is gaining foothold. There is no point in full hybrids that don't have electric continuously variable single-speed planetary gearset transmission, or in full hybrids that don't have Atkinson cycle engine.
A plug in hybrid is similar to a regular full hybrid, but with these differences: the battery may be charged, the battery is far larger, between 8-20 kWh, the battery is almost always lithium ion, and the battery allows providing more power, so much that full fast acceleration on battery power only is possible. Usually electric-only operation is allowed at all reasonable speeds, up to 120-130 km/h. Electric-only range is between 15-60 km. Optimally the engine would be Atkinson cycle and there would be similar electric water pump, electric A/C unit, electric continuously variable planetary gearset, etc. but some manufacturers other than Toyota are combining plug-in hybrid operation with non-Atkinson cycle engines and traditional transmissions. In these cases, the manufacturer usually markets the car with something like "20 g/km emissions, 0.9 l / 100 km fuel consumption" and doesn't tell that while the fuel consumption when driving only on electricity is 0.9 l / 100 km, if you drive on gasoline the fuel consumption skyrockets to over 10 l / 100 km. Also quite many plug-in hybrid cars have strict restrictions on cold operation: it may not be possible to drive only on electricity if the temperature is freezing. Some good plug-in hybrids (i.e. Toyota) allow full electric operation when cold, and also have very low fuel consumption when the battery is empty and electric-only operation therefore is impossible.
Regular hybrids tend to have a small Li-ion battery, say 4kWh, and a low-power motor (actually it tends to be something like an upgraded starter motor). It charges the battery with energy generated during braking and cannot be independently charged. The motor can power the car at low speeds in traffic, and also start the engine and provide power for ancillary electricals.
A plug-in hybrid or PHEV typically has a larger Li-ion battery, say 10-15kWh, and a much more powerful motor. As a result a PHEV can be propelled by electric power alone, for a typical range of 30-40 miles. As the name suggests, you plug it in to charge the battery (although it still uses regenerative braking to top it up). The engine cuts in when the battery is depleted or the motor is under heavy load.
The figures often quoted for PHEVs are now coming under serious dispute - this article suggests that real CO2 emissions are around 120g/km, instead of the quoted average of 44g/km. Some more realistic assessments are available at the GreenCap website and Emissions Analytics website. Part of the problem is that drivers don't actually need to charge them and can drive around almost entirely on petrol power. It is highly likely that many are bought as company cars due to their low tax rates, but are never actually charged.
And it gets worse - as the petrol engine can be suddenly called upon to start up and immediately be placed under heavy load, the emissions of other pollutants such as VOCs can be worse than diesel vehicles (see this article.)
Also, you have the added complexity and maintenance requirements of having both a regular and EV powertrain in the same vehicle. So in no way are PHEVs "as good as" pure EVs.