Compression in JPEG files in digital cameras

I need some help in explaining the JPEG compression feature in digital
cameras. My camera (which likely is similar to most others) has the
feature to compress the photo JPEG files in the storage card. It also
has the choice to have different pixel sizes (example: 3000x2250,
2000x1500, 1024x768, etc). What is the difference of the above two
features? If you store a 3000x2250 pixel data in compressed mode,
does it loose its quality? Can it be re-instated to full uncompressed
size without loosing photo quality?. When I compressed the data, it
will fit more pictures in a single storage card. But, is it the same
if I choose 2000x1500 pixel and no compression instead?
Thanks for info.