Have 1 steam (CB Activity Field, menu item, or override the Activity tab) with an Asset set to "user" then have another with an Asset set to "user.connectionsonly". You may need to use "self" and "self.connectionsonly" depending on where this is being output.

In creating a CB Activity Field how do I identify and what do I select to assign "self" post from "self.connectionsonlyt"

For Activity fields you're fine to use "user" and "user.connectionsonly" for the Asset.

How would I override the Activity Tab

Edit the Activity tab within CB > Tab Management. You can override all of its parameters there; including Asset.

Where do I locate the Asset to modify it to "self" and "self.connectionsonly"

You don't modify anything. You just set the asset literally to "user" (only shows your activity) or "user.connectionsonly" (only shows your connections activity) without quotes of course.