What is the conceptual difference between sustainable and responsible consumption, if any?
Sustainable Consumption and Responsible Consumption are complementary terms. Perfect sustainability means minimal environmental burden, which often leads to a reduced quality of life and sometimes, ironically, increased input consumption. Responsible consumption takes into account more factors including quality of life & resource use over time but still does so in the most efficient terms possible. Thinking through both should give the best of all worlds.
For example, if an older, still working refrigerator is replaced with a newer, more energy efficient model it involves increased production & disposal costs to the environment but since the energy saved & feature benefits are tremendous it mostly offsets the burden. If someone sets aside a poorer quality stock pot that has to be replaced yearly for a much sturdier/more heat efficient pot that will use less cooking energy, burn food less often & last many, many years before needing replacement, strictly speaking, it's a non-needed purchase but again, decreases material use overall such that it's actually the more responsible choice. There are many, many more real-world examples, but these will get you started in a helpful decision-making path. Good luck with your process!
Perhaps it's just a simple difference: It would be irresponsible to deny a plastic bottle of water to a person dying of thirst, however it is unsustainable to use plastic bottles that go to landfill.
Therefore you could argue that some responsible consumption is unsustainable.
I see sustainability as being a long term issue; we need to change our actions now to avoid long term problems. From a big picture perspective, it is perhaps less useful (dare I say it, even irresponsible, in some cases) to try to live a 100% sustainable life now because doing so may reduce the chance of solving long term sustainability problems for a greater number of people. I say this because those of us that understand the need for sustainability need to be able to help educate and set a visible example to others.
It might be sustainable to retreat to a self-sufficient life in the remote countryside, shun unsustainable technology, and refuse to use life-extending unsustainable healthcare systems, but that is unlikely to help encourage others to be more sustainable due to its lack of visibility and its extreme differences to more common lifestyle choices. It may be better to live a less sustainable, but more visible, lifestyle while still being substantially more sustainable than accepted norms. Constantly pushing that boundary over time may be the best way to get everybody living more sustainably.
To get to the point, it makes some sense that an end goal of sustainability justifies an unsustainable means to get there.