What is the difference between random access and serial access?

This is what my teacher told has told me, but I found it confusing:

*Serial access writes to the end of a file and the whole file is overwritten when edited (and saved).

*Random access only changes relevant date, making it more efficient than serial.

But for some reason I feel that he may be wrong about the ‘overwritten’ part, and this makes me doubt how accurate his above descriptions are.

Could someone please clarify for me?