Correct, both are throttled. The limits are less than 10/day, iirc. They also depend on your auto confirmed status. We've unfortunately had the feature abused badly in the past.

If you need to send more, you need to get your account approved as a bot, or put on the throttle exemption list. That will probably require some community discussion about what you're doing and what you need, then a bureaucrat can give you right.