Hi there, gman91478.
I see that you're having a problem when sending iMessages to a contact from your Mac. You added their new number to their old contact card and the messages on your iPhone stayed together. Now, they've been separated on your iPhone and Mac, and I'm glad to help.
About iMessage and SMS/MMS -- If they've separated, have a look at the color of the text bubbles in each. If you're seeing one thread has blue text bubbles, and the other is green, one is being sent by iMessage and the other is sent as SMS/MMS.
How to forward SMS/MMS text messages from your iPhone to your iPad, iPod touch or Mac -- Since you need a text message plan in order to send and SMS/MMS message you can use Text Message Forwarding between your iPhone and other devices. I'm not sure if this will merge your current threads together again, but it should moving forward.
Keep all your messages in iCloud -- You can also use iCloud to sync your messages between all of your devices.
Use Continuity to connect your Mac, iPhone, iPad, iPod touch, and Apple Watch -- This article explains all of the other features of Continuity.
Take care.