As far as I know, there's no way to install the Homebrew package manager without root.
But if your goal was to install Bitcoin Core, I'd recommend pulling the source through git (like you've done) and building it locally, anyway.
I pulled the source through git. I will like to ask is $brew command line doing the same thing $ sudo does ? Because pip isn't install anything for me on my mac command terminal
All of your questions can be answered through simple web searches.
brew: OS Package manager.
apt: OS Package manager.
pip: Python package manager.
sudo: Execute command as superuser / root.
git: Version control system / VCS.
And how to enter your password on the command line is what I've answered in the very first reply. Was something unclear about that?
One more clarification: Installing Homebrew requires root; using it after it's installed does not.
https://github.com/Homebrew/install/blob/master/install.sh#L220So you're looking at installing Homebrew through
sudo /bin/bash -c ... and then using it afterwards simply with
brew install ....