The devices in the Apple ecosystem are famous for the multiple possibilities of interaction and synchronization, all through the iCloud account. The pictures, the music, the marks of Notes, Reminders, Calendar, Contacts And even the messages are automatically synchronized between all the devices on which the same Apple ID is authenticated. As for the messages, there is a difference, which is why I do not receive SMS on Mac or iPad, but only Imesassages.
In an article I showed what is the difference between the two types of messages, iMessages si SMS, which we receive on the iPhone in the Messages application.
The messages received / sent between iPhone users are done through Apple's Imessage service. When we make an Apple (Apple ID) account, associated with the email address is also a phone number. The transport of this type of messages is done through the Internet and have no connection with the SMS messages that are through the mobile operator. Which is why users do not receive SMS on Mac.
When you receive a message of Imassage type, it will automatically reach all the devices you have the same Apple ID. Mac, iPad, Apple Watch and iPhone.
Why don't I receive SMS on Mac and how do I solve this problem?
Iphone users can send and receive SMS on Mac, iPad or Apple Watch, but SMS is required to be redirected from iPhone to devices. This option does not involve costs. It is a redirection between devices.
To activate the option to receive and send SMS from Mac, the tutorial below is helpful.
Go on iPhone in Settings → Messages, then to Text Message Forwarding.

At "Text Message FordWarding" you have a list of Apple devices that you can redirect SMS. So when you receive an SMS on the iPhone, it will automatically come on Mac or iPad.

Like the iPhone, the messages conversations on iPad and Mac will be blue for immesaage and green for SMS.