Most of the issue you raised would be treated in the second part of this post.

To your question;

What's the distinction between a role model and a mentor?

A role model is someone who you pattern your life after, it could be someone you have access to OR otherwise.

On the other hand,

A mentor is someone who has achieved what you hope to achieve, they make inputs in your life, they're actively involved in your journey to the actualization of your goals. They have to be a part of your life, not some distant personality.
I hope I was able to give you clarity, thanks for stopping by.