Fair enough. It is difficult to make a distinction of the two terms if we don't have another term. I had started writing about how difficult it was to find a term to substitute the common-usage of responsibility. Then a possibility popped up.
The rules-based, considered-in-advanced "responsible choice" is more akin to expectations and standards. That is, one's outwardly measurable behavior can be observed and held up against a standard. This is the typical way a child is socialized.
The other, responsibility in the sense of accepting-the-consequences-of-your-actions-and-moving-on-from-there falls more along the lines of, "with great responsibility comes great power." It's really the language of power (and as a side-effect, freedom and resources). It's choice after stripping away the social expectations.
I have discovered (and experienced) a way to teach a child how to make choices, accept its consequences, and move from there. It requires a teacher who has been initiated in this. When the child makes a choice, the teacher engages in a conversation to probe the motivations. Is the choice really Choice, or are there some underlying hidden agendas. (For example, the child might be thinking, "If I do this, then Dad will be proud of me, and I will feel accepted."). It's only when these hidden agendas are stripped away from the child, then the teacher points out that this is Choice. "Ok. You chose this. Here is what you do."
The teacher then shows a little bit of the practice to accomplish it, and then sits there with the student and let the child do it. (Not read a book, not watch Netflix, not go away and leave the child to it; the presence of mind of the teacher witnessing is actually very important). It is very important that the teacher never hold the child's hands. If you've stripped away all the hidden agendas and motivations, then if you hold their hand, they are not really accepting the consequences of Choice. You're not accepting their Choice. It is, however, OK, to answer questions, to correct incorrect attempts after the fact (typical newbie mistakes like, forcing things, or going too fast, and sometimes demonstrating something once the child has tried it first).
It's even ok if the child feels overwhelmed by the Choice. That's actually an awesome initiation. The typical response is to seek an adult figure to do it for them. This is where the teacher maintains discipline: the child has to do it for himself. Reminders that, "you chose this" often helps. Usually, the child is not really struggling with the challenges of task or skill, but rather, struggling with inner aversions and inability to accept the suffering that comes with the work.
However, when the child gains some achievement in the task, he knows for sure that it wasn't because people did it for him. He knows it wasn't because someone else expected it of him. He knows it resulted from his effort. He knows to his bone, he chose to do something and he did it himself. External praise isn't required. (What's the point? You know you accomplished it, the presence of praise from the outside is irrelevant). Often though, continued discipline to have the child keep practicing is needed. (Once is not enough, that's why it is called "practice"). Usually, as the skills mature, and as the child matures, the child grows into adulthood with the capability of disciplining himself.
If it sounds intense and a lot of work, it is. It requires a lot of attention from the teacher. It's not scalable. In fact, this dynamic is closer to the older master-apprentice model of instruction (assuming the master didn't have his own hidden agendas).
What you end up with though, is someone who knows how to grow into tasks bigger than himself.