Deflate (as used in gzip) uses a Huffman coder. LZMA (as used by xz) uses a predictive range coder. Zstandard can use either Huffman or FSE. Some high-speed compressors like LZ4 skip the entropy coding stage entirely at the expense of compression ratio.
Bzip2 is an interesting aversion of this pattern - it uses the Burrows-Wheeler transform as a first pass instead of LZ. Unfortunately, this is one of the major reasons why it's so slow.