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Guilt - I did something wrong and feel bad about doing it.

Shame - I did something wrong and I feel bad about myself.

Remorse - I did something wrong and I'm sorry for doing it.

Regret - Something happened - maybe caused by me, but maybe not - and I wish I had done something differently.

These things can overlap, but that's the general gist of it.

Remorse and guilt seem like the exact same thing, or am I missing the presence of a gap between feeling bad about doing something, and being sorry you did it?

There is a gap, yes. Guilt is about the action itself, remorse is about the victim of the action. Guilt is I shouldn't have done punched a person in the face because punching people in the face is wrong, remorse is I shouldn't have punched you in the face, because it hurt you and I'm sorry for hurting you.

It's entirely possible that you can feel guilt about an action but not remorse, or vice versa.

• Maybe I don't like a person and while I know punching people is wrong, I don't feel bad about them getting punched. That's guilt, but not remorse.
• Maybe I do like a person and while I don't care that punching people is wrong, I feel bad that I hurt that particular person. That's remorse without guilt.
• Maybe I punched somebody and feel bad about both the action and how it affected somebody. That's both guilt and remorse.
• Maybe I punched somebody and don't care that it's wrong or that I hurt them. That's psychopathic neither guilt nor remorse.

Guilt is knowing you F'd up.

Shame is knowing that other people believe, or at least they perceive, that you F'd up (you can personally believe you didn't).

Remorse is wanting to make whatever you F'd up, right again.

Regret is when you can't make what you F'd up, right - no matter how much you want to.

Guilt and remorse are hard to compare and explain imo! I wouldn’t agree with the other comment that it is about the victim.

When I am trying to understand the meaning of words I like to look at the history of the way the word was used and if it’s changed over time.

https://www.etymonline.com is the best website I’ve found for this.