conda list to be sure, but I’m guessing there is no pip in your environment, so it picks up the global one.
conda install pip should take care of it.
Actually, that probably will fail, if pip is not installed – but that’s good advice in general, in this case, you want the failure, rather than the wrong pip.
Note that invoking pip via python -m has been the recommended way to do it for years – even without conda there are many ways to get out of sync!