Notes are stored in XML files. “Notes_(username).xml” in Paratext 8 and “Comments_(username).xml” in Paratext 7. If you copy the note file to another project folder, those notes will appear in that new project. If the project text is different in the new project, the note flags might not be attached to words in the text but all appear at the beginning of the verse.
There are syntax changes between notes in Paratext 7 and Paratext 8, so you cannot copy a notes file from 7 into an 8 project and have it work. You might be able to make a backup to file of a 7 project, then restore from file in 8 and select the note files to have them transfer over.