I am writing a basic python script and I am trying to use the Github API. Because I am new to the development scene, I am unsure of what I can share with other developers. Do I generate a new personal access token (that I assume can be revoked) or do I give them Client ID and Client Secret?
Can someone explain how OAuth (Client ID and Client Secret) is different from a personal access keys? 
Does this logic work across all APIs (not just on Github's)?
The Short, Simple Answer
You should probably give them none of those things. They are equivalent to handing over your username and password to someone.
The Longer Answer
It depends...
Personal Access Tokens
Your personal access token is a unique token that authorises and represents you during API calls, the same way that logging via the web interface authorises you to perform actions there. So when you call an API function with a personal access token, you are performing that API action as if you yourself had logged in and performed the same action. Therefore, if you were to give someone else your token, they would have the same access to the site as they would have if you gave them you username and password combination.
Personal access tokens have attached scopes. Scopes control exactly how much access to GitHub a particular token has. For example, one token my have access to all private repositories, but another token only to public ones.
Client IDs
A client ID represents your application, rather than you. So when you create an application, GitHub gives you an ID that you use to identify your application to GitHub.
Chiefly this allows someone logging into your application using OAuth to see on the GitHub web interface that it's your particular application requesting access to their account.
Client Secrets
A client secret is a random, unguessable string that is used to provide an extra layer of authentication between your application and GitHub. If you think of the client ID as the username of your application, you can think of the client secret as the password.
Should I Share Them?
Whether you wish to share any of these things depends largely on how much you trust the other developers. If you are all working on the same application, it's likely that you will all know the client ID and client secret. But if you want to develop an open-source application that people will install on their own machines, they should generate their own client ID and secrets for their own instances of the app.
It's unlikely that you should ever share a personal access token, but if you have a bot account used by the whole team, then sharing the tokens could also be okay.
Personal Access Tokens, User Tokens