Quick format will remove files from the partition and rebuild the file system, volume label, and cluster size. It's faster than full format. but It just destroys the journal that keeps track of the files and their location on the hard drive. So, the data is still on the hard drive and can be easily recovered by data recovery software.
Full format will completely remove files from the partition, rebuild the file system, volume label, and cluster size, and scan the partition for logical bad sectors. that's why full format is slower than quick format.