If I'm personally invited to give a talk but have to pay and submit an abstract does that count as a invited talk? Suppose I receive a personal, written invite to a conference. I would like to attend, and the procedure still requires me to submit an abstract and pay for the conference, would that count as an invited talk?

On one hand, it's not different procedurally from someone submitting an abstract that gets accepted. But on the other hand, I have technically been given what seems to be an invite.
Yes. It does count. For example, many meetings have special topic sessions (e.g., SETAC). When people organized these sessions, they are often required to have a number of committed speakers. 

That being said, here are some caveats:


Beware of predator conferences.
The value of being invited to a special session is different than being invited as a plenary speaker. Be careful to not overplay this on your CV. For the life sciences, invited talks are nice, but not as import as fields where conference proceedings are highly valued.
The custom related to being an invited talks vary across academic disciplines.  Also, some meetings wave registration for all speakers (e.g., ODSC). Most, however, do not.