The most important difference is that gzip is only capable to compress a single file while zip compresses multiple files one by one and archives them into one single file afterwards. Thus, gzip comes along with tar most of the time (there are other possibilities, though). This comes along with some (dis)advantages.
If you have a big archive and you only need one single file out of it, you have to decompress the whole gzip file to get to that file. This is not required if you have a zip file.
On the other hand, if you compress 10 similiar or even identical files, the zip archive will be much bigger because each file is compressed individually, whereas in gzip in combination with tar a single file is compressed which is much more effective if the files are similiar (equal).