What is the difference between primary groups and supplementary groups?

Question

Accepted Answer

A user has exactly one primary group (the GID in /etc/passwd, used as the group-owner of files they create) and any number of supplementary groups (listed in /etc/group) that grant extra access.
The practical difference: the primary group decides the group ownership stamped on a brand-new file; the supplementary groups are just additional memberships the kernel checks when deciding group permissions. For checking file access the two kinds are treated identically — if you're in the group at all, you get group permissions.
Primary Group:

Stored in /etc/passwd (4th field)
Created automatically with same name as user
Used for new files created by user
Visible in ls -l output

Supplementary Groups:

Listed in /etc/group
Provide additional permissions
Can belong to many groups

Example:
labstudent:x:1004:1004::/home/labstudent:/bin/bash
           │    │
           │    └── GID 1004 (primary group)
           └── UID 1004

View groups:
id labstudent
# uid=1004(labstudent) gid=1004(labstudent) groups=1004(labstudent),10(wheel)

/etc/group format:
groupname:x:GID:members
wheel:x:10:packer,sysmgmt,florian,labstudent,labadmin

Key insight: For file permissions, primary and supplementary groups are treated equally - if you're in the group, you get group permissions.