File archiving means to combine multiple files together for easier management of the data (i.e. backup, mail attachments, sharing by FTP, torrent, cloud, or any kind of network service, etc) as for the host filesystem all the data will be treated as a single file rather than as multiple ones, eliminating the overhead of handling multiple objects - for each single file, locating the physical data on disk, locating possible fragments, checking file level security permissions, and so on.
File compression means to reduce size of data on disk encoding it to a smaller output, employing various strategies to efficiently map (most cases of) a larger input to a smaller output, i.e. using statistical analisys to reduce redundancy in inputa data.
Data compression, too, predates development of ZIP standard, as once the input files were merged into a single output archive, the operation was often concatenated to lossless data compression to reduce the size of the archive using various utilities available at the time as SQ (DOS, CP/M), CRUNCH (CP/M), and compress (Unix).
TAR format, for example, is still an uncompressed archive standard, and uses external compressors, nowadays usually GZ (fast deflate based compression, same as in ZIP format), BZ2 (more powerful compression), XZ (modern, very powerful LZMA based compression - the default compression algorithm used in 7Z format), BR Google's Brotli (modern, very fast compressor), and ZST Facebook's Zstandard (another modern, very fast compressor).
Learn more about similarities and differences in Lossless data compression and Lossy data compression. For general purpose compressed archive file, however, compression means Lossless Compression, a 1:1 mapping of input to a smaller output.
SEA's ARC format (1985) combined the archival and (lossless) compression in a single pass, providing probably the first example of general purpose of archive manager, which allowed both to spare storage for backup, and save upload and download bandwidth (and time) for sharing - at the time, mainly BBS.
A few years later, after a controversy with SEA about alleged derived work in PKARC, Phil Katz superseded previous works releasing PKZIP, which knew great success due multiple factors, as superior speed and efficiency, and being the specs released under public domain, and having relatively few competitors in years of fast PC market expansion.
ZIP format is a lossless data compression and archival format created in 1989 by Phil Katz, implemented for the first time in PKWARE's PKZIP.
The ZIP file format specifications were released under public domain and the format had long and lasting success, to the point often "zip" is colloquially used for any generic compressed archive, and many package formats are based on deflate compression and/or same or very similar specs: Java JAR / WAR / EAR, Android APK, Apple iOS IPA files (iPhone and iPad devices), Microsoft CAB and Office compound files. WinZip 12.1 (2009) introduced the new ZIPX file format specifications for identifying a new archive standard which supports newer and more powerful compression algorithms.