RFC 1950 - zlib
RFC 1951 - raw deflate
RFC 1952 - gzip
The $encoding parameter referers to the window bits. So you can encode in several formats:
<?php
// RFC 1950 - zlib
$compressedData = zlib_encode($uncompressedData, 15);
// RFC 1951 - raw deflate
$compressedData = zlib_encode($uncompressedData, -15);
// RFC 1952 - gzip
$compressedData = zlib_encode($uncompressedData, 31);
?>