Yes, you'll lose quality when converting to JPG (as opposed to PNG). Some image editors allow you to specify what quality to use (for example, 0-100) so you have some control over how much is lost.
I can open a random ~600 KB PNG screenshot and save it as a JPG using quality setting 100 => results in a 385 KB JPG and I don't really see any differences in this one (they're there, though

) or I can save it with quality 85 (the default in the program I use) => results in a 90 KB JPG and looks ok, but with a noticeable difference.