How is rm command different from the delete button?

Your understanding is essentially correct - the Del key as used in Nautilus (or other file manager) is NOT the same as using rm; it "moves" the file to Trash instead so that it can be recovered unless you Empty Trash (which is the same as rm).

Note that even if you rm a file, the actual data is still on the disk after the inode is deleted. If you act immediately before the data is eventually overwritten, you can still recover the data using a tool such as testdisk/photorec.