Meh, iWatch and iMessage are surefire ways to get people to think of the right product. Technically incorrect terms, but they'll get the message right.
The iOS client has been “Messages” since iPhone OS 3.0; before that it was called “Text” and had “SMS” written inside the chat bubble in the icon. iMessage wasn’t introduced until iOS 5.0.
The macOS client was originally “iChat”, then “iChat AV”, then “iChat” again; in this era it supported multiple protocols including AIM and Jabber. In OS X 10.8, the client was renamed to “Messages” and gained iMessage support in addition to the older protocols. Support for the older protocols was removed in the just-released macOS 10.13.
[1] With a delightful/odd error message: "The targeted service Potato has been discontinued".
It would be less weird to refer the “apple phone”.