I work in a laboratory and I am terrified of making any mistakes...I feel like I'm always asking for clarification or confirmation
That’s interesting. Have you considered that rather than finding you ‘ditsy’, your colleagues think that you are one of those people who won’t make a decision in case the decision is wrong? That by asking colleagues to effectively tell you exactly what to do, you shift the burden of responsibility onto them? They might regard you as putting on a ‘helpless’ act, even if you are not, in order to avoid owning your work fully.
which on the one hand is good because I haven't made any mistakes yet, but on the other hand it does make me come across as less competent than my colleagues.
Truthfully? You are probably right.
On the other hand, my colleagues are more confident and will do things without thinking it through and they have made several mistakes. I'm not sure which is worse; I guess it would be best to be somewhere in the middle of those two approaches.
Truthfully, your way is worse. Enough for your line manager to specifically bring it up:
My supervisor actually brought it up to me after I apologised for nearly making a mistake and said I need to not worry so much, mistakes will happen in this environment and when they do they will be safely dealt with.
Quite right.
I have a team member who strenuously avoids making decisions and expects me to (1) tell him what to do and (2) review his work plans before he executes them. He’s a qualified and experienced finance professional and I shouldn’t need to be doing this. Do I consider him to be the make equivalent of ‘ditsy’? Yes, in the sense that he expects other people to do the thinking for him so that he can never be held liable for mistakes.
Don’t be one of those people. Do everything you can to build up your confidence in your work. Write everything down, revise it nightly, do whatever you have to do. Otherwise your colleagues’ patience will wear thin.