This is the friendliest error in Minecraft: it tells you exactly what is wrong and which side is behind. The only decision is whether the player updates or the server does.
What you are seeing
Outdated client! Please use 1.20.4Outdated server! I'm still on 1.20.1- Some players can join and others cannot.
Why it happens
Minecraft's network protocol changes between versions and does not negotiate. The message names the version the server is on, and the direction tells you who is behind: «Outdated client» means the player is older, «Outdated server» means the player is newer.
What to do
- Read which version the message names
That is always the server's version. It is the number the player has to match.
- Have the player switch profile version
In the Minecraft launcher, edit the installation and pick the exact version the message named. This is the fix in almost every case.
- Or change the server, if most players are already newer
Changing the server version is the bigger move — see the article on doing it safely, because your plugins and your world are involved.
The player connects without the message. Their client version and the server version now match exactly.
If you want one server to accept several client versions, a protocol bridge such as ViaVersion does that. It is a plugin, not a setting, and it has its own quirks — there is an article on those.