Recommended way to install pip(3) on centos7

1. Is pip the same for 3.4+

   No, it's not. A single pip installation serves a single Python distribution (pip2.7/pip3.4/pip3.5 etc).

2. Since Python 3.5, pip is already bundled with the python distribution, so you can just run python3.6 -m pip instead of pip.

3. Python 3.6 is not available in CentOS 7 vanilla repo. I usually resort to IUS repo when needing to install a fresh Python on CentOS. It always has the most recent Python version, the current one being 3.6.5. It also offers a correspondent pip package.

   $ yum install https://centos7.iuscommunity.org/ius-release.rpm
   $ yum install python36u python36u-devel python36u-pip
   

   Unfortunately, IUS doesn't offer a package for Python 3.7 yet so if you are looking for Python 3.7 on CentOS 7, building from source is your only option.

Edit: when yum is not an option

You should prefer the bootstrapping solution described in this answer as it is the most reliable way to get a working pip installed.

To install pip for python 3.6 on CentOS 7 you need to run

$ python3.6 -m ensurepip

Follow these commands in Centos 7

yum install python36
yum install python36-devel
yum install python36-setuptools
easy_install-3.6 pip

to check the pip version:

pip3 -V
pip 18.0 from /usr/local/lib/python3.6/site-packages/pip-18.0-py3.6.egg/pip (python 3.6)