Hey R.Shepherd,
Welcome to Apple Support Communities. The information below may help with your question.
"If you block someone on one device, they’re blocked on all Apple devices signed in with the same Apple ID." For more details, review this article: Block calls and messages from certain people.
Since that is the case, make sure the Apple ID and phone number are the same in Settings > Messages on the iPhone and Messages > Settings > iMessage on the Mac.
We ask that you check this information to make sure the phone number is the same on both devices. If they are not the same, that may explain why one device is sending iMessage and the other is sending SMS.
Also, if you are blocked, the contact wouldn't receive your call. To confirm, test by placing a call to that contact.
Best wishes.