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.

Summarised from another site:

Core package repositories for CentOS 7 does not have python-pip. For that you need to enable an EPEL ("Extra Packages for Enterprise Linux") repository. You do that with

sudo yum install epel-release

After that, you should be able to install pip with

sudo yum install python-pip

Also possibly related:

• How to install pip in CentOS 7? (on StackOverflow, old)
• Recommended way to install pip(3) on centos7 (on StackOverflow, newer)

In particular, one answer there states that

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