Texting from a Mac Laptop

To elaborate a little on what Barney said, to set up your Mac to text to both Apple and non-Apple device users, you need to coordinate the settings on both the iPhone and the Mac together. Without the iPhone around to do this, as Barney noted, you can still send and receive text messages but only to other Apple device users. Most of the settings have to activated, in fact, on the iPhone:

iMessage checklist

iPhone and Mac both logged in to same Apple ID. Try logging off and logging on if necessary.

iPhone Settings => Messages shows iMessage as "on" (sometimes toggling this off and then on fixes some things)

iPhone Settings => Messages shows Send & Receive showing both phone number and email (Apple ID)

iPhone Settings => Messages shows Text Message Forwarding and your Mac is listed and shown as "on" there.

iPhone Settings => Messages shows Send as SMS "on" and MMS Messaging and Group Messaging both "on"

On the Mac: Messages => Preferences shows same and correct Apple ID and "You can be reached for messages at" indicates both phone number and Apple ID (email), and "start new conversations from" indicates the phone number.

* Don't see the Text Message Forwarding setting on your iPhone? Go to Settings > Messages, turn off iMessage, turn it back on, tap Send & Receive, tap Use Your Apple ID for iMessage, then sign in with the same Apple ID used on your other devices.

How to forward SMS/MMS text messages from your iPhone to your iPad, iPod touch or Mac - Apple Support

Your Mac can only send messages over the iMessage protocol.

In order to send to people who don't have any Apple devices, it sends via standard SMS over the cell phone network. It needs your cell phone to send the messages via SMS.

Blue contacts are iMessage capable. Green ones are not.

And, your Mac and iPhone need to be on the same network/nearby each other.

If it is still in the shop, you can't use it to send SMS.

Yogacats wrote:

This makes sense. Thank you.

But, since iPhones use iMessage and my MAC can send and accept messages over the iMessage protocol, why can't another iPhone user send a new message to me (my MAC)? They've been able to "respond" to a message sent from my MAC, but when they try to initiate a new text to me, to start a new text thread, the system only offers my gmailI. It doesn't offer the capability to text me...? I apologize if I sound ignorant, I'm just trying to understand this scenario.

If they are using an iPhone, you should be able to receive an iMessage on your Mac. If your gmail is your iCloud username, then that is your iCloud account. Your Mac doesn't have a phone number.

Open Messages Preferences > iMessage tab. There are options for how you can be reached.