Update a local branch with the changes from a tracked remote branch

You don’t use the : syntax – pull always modifies the currently checked-out branch. Thus:

git pull origin my_remote_branch

while you have my_local_branch checked out will do what you want.

Since you already have the tracking branch set, you don’t even need to specify – you could just do…

git pull

while you have my_local_branch checked out, and it will update from the tracked branch.