Messages---contact Red on MacBook, Green on iPhone

That person apparently does not use iMessages but only SMS messages. If that's the case, you need to connect your phone to your Mac to be able to message them from the Mac. On the iPhone, go to Settings>Messages>Text Message forwarding and select your Mac. Note that both devices must be signed into the same Apple ID.

See also:

Forward SMS/MMS text messages from your iPhone to your Mac or iPad - Apple Support

This article is for the iPhone, but may help:

What is the difference between iMessage and SMS/MMS? - Apple Support

My understanding:

• SMS messages use text message service from your phone company.
• MMS messages use text message and cellular data service from your phone company.
• SMS and MMS are a "lowest common denominator" between many kinds of cell phones, including Android phones, and even dumb phones (many of which can at least send or receive SMS).
• iMessages are enhanced messages, between Apple devices, that travel over the Internet.
• Your Mac needs help from your iPhone to send or receive SMS/MMS messages, because it does not have a cellular phone network connection of its own.
• Your iPhone prefers to use iMessages when talking to other iPhones, but if either phone is offline, message delivery will fail, and then you'll get the option to retry or to fall back on SMS/MMS.

I went to my iPhone text message forwarding. I turned it off and right back on. It started working immediately.