I'm not really sure they are fundamentally different in principle. In effect both involved a person being refused a service because of their political opinions.
No. The Asher's case is explicitly not that. They refused to bake the cake because it had a message on it supporting gay marriage.
I think it is pretty clear that someone asking for a cake supporting gay marriage is doing so because they ... err ... support gay marriage.
Not necessarily. Somebody who was against gay marriage might order the cake for their gay friends because they put their friendship above their political views.
And I don't think Ashers had a policy of refusing to bake any cake with a message that is a political belief - so the reason they refused in this case was because they disagreed with the political belief of the person asking for the service.
They disagreed with the political belief they were being asked to put on the cake, not because of the beliefs of the person making the order.