From "man 2 SOCKET":
SOCK_STREAM Provides sequenced, reliable, two-way, connection-based
byte streams. An out-of-band data transmission mecha‐
nism may be supported.
SOCK_DGRAM Supports datagrams (connectionless, unreliable messages
of a fixed maximum length).
SOCK_SEQPACKET Provides a sequenced, reliable, two-way connection-
based data transmission path for datagrams of fixed
maximum length; a consumer is required to read an
entire packet with each input system call.
Based on the source code you linked, it appears that "unix" uses SOCK_STREAM, "unixgram" uses SOCK_DGRAM, and "unixpacket" uses SOCK_SEQPACKET.
Hope that helps,
Peter