Command history in zsh

You've probably got INC_APPEND_HISTORY set.

The INC_APPEND_HISTORY option, from man zshoptions:

This options works like APPEND_HISTORY except that new history lines are added to the $HISTFILE incrementally (as soon as they are entered), rather than waiting until the shell exits.

The option that you want is APPEND_HISTORY:

APPEND_HISTORY If this is set, zsh sessions will append their history list to the history file, rather than replace it. Thus, multiple parallel zsh sessions will all have the new entries from their history lists added to the history file, in the order that they exit. The file will still be periodically re-written to trim it when the number of lines grows 20% beyond the value specified by $SAVEHIST (see also the HIST SAVE BY COPY option).

You can read about these options in the man zshoptions, man zshall or online here.

To set them, in your ~/.zshrc or similar, you should have:

setopt APPEND_HISTORY

Be aware that, if you're using oh-my-zsh by default, I believe, INC_APPEND_HISTORY is used. I'm not 100% sure which way around things get loaded, but if the oh-my-zsh option overrides the one you've set in ~/.zshrc, you can fiddle with it in ~/.oh-my-zsh/lib/history.zsh

To add to the accepted answer, if you use oh-my-zsh, you probably have SHARE_HISTORY option enabled by default.

To achieve separation between running shells + entire history combined in a newly opened terminal, you have to comment or remove the following line:

setopt share_history # share command history data

from ~/.oh-my-zsh/lib/history.zsh