Am I in RHEL or OEL?

OK, first time accessing a client, and you have this question?

# RHEL:

[grepora-rhel-server]$ rpm -qf /etc/redhat-release 
redhat-release-server-6Server-6.9.0.4.el6.x86_64

# OEL:

[grepora-oel-server]$ rpm -qf /etc/redhat-release
enterprise-release-5-0.0.2

You may also have some other options like:

[grepora-fedora-server]$ rpm -qf /etc/redhat-release 
fedora-release-20-3.noarch

Hope you enjoy it!
Cheers!