What is the difference between the two?
Added to Opportunity triggers when the person is first added to the opportunity. Opportunity is Updated triggers when a field on the opportunity changes after a person has already been added.
I see that there is also a "Has Opportunity" how does that one differ?
That's a filter, not a trigger, so it runs as scheduled. It looks at the current state for that person (do they have an opportunity at this particular moment with whatever criteria I added), but it doesn't run at the moment a person is added to an opportunity or when the opportunity is updated, like the triggers do.
Many times you need to use both Added to Oppty and Oppty is Updated as triggers.
For example, you might be trying to find people who become customers.
Filter and Segmentation
Has Oppty is a filter that gives you a point in time snapshot of anyone sitting in inventory with an Oppty. I actually like to use this as part of a segement as a person could have multiple opportunitie with multiple stages.
The key to the Segement is determining which one wins? Order of the segement is important. Foir example, a person could become Lost and later become Oppty if a new Oppty is opened. The order I usually use: