The tense and aspect are different. "Have written" is present perfect, whereas "wrote" is simple past. This website explains it pretty well.
Present Perfect refers to completed actions which endure to the present or whose effects are still relevant.
Use the past tense to indicate past events, prior conditions, or completed processes.
In these examples, you could say #1 and #3 whereas #2 and #4 are incorrect.
- I have written a letter. Would you like to review it?
I wrote a letter. Would you like to review it?
I wrote a letter yesterday.
- I have written a letter yesterday.