You're sending an email, not a SMS. That's the popular interpretation of "text messages". Also it may be free for you to send (because it's not a SMS) but not free for your recipient depending on their carrier/plan.
Here is Twilio's official docs (arguably the most popular platform in that field): https://www.twilio.com/blog/how-to-send-sms-online Would you say that it's misleading because you are actually sending an HTTP request, not an SMS? If you use the Python wrapper, would you say what you're doing is calling a Python function, not sending an SMS?
Do you think their pricing page is incorrect, because it doesn't include the price the recipient might have to pay, for each possible carrier they might be using?
I mean, where do you stop? When you pay your ISP, should the bill show "pushing the button to activate your connection", rather "internet service"? Should coffee shop include the cost of a bottle of water, because drinking coffee will dehydrate you? I don't understand what you expect.
I see your point, but I think rather than it being misleading, you're just interpreting it differently. The way I see it since the recipient is receiving a text - that's using the SMS protocol even if it is through a gateway. The result doesn't change.
As to the second point, yes - I did mean free for the sender. I assumed that people were aware that the recipient can still be charged. I mean by the same logic, you might as well add the recipient's phone bill (if they don't pay per SMS message individually) and even the cost of their phone if you want to be picky. I don't think anything is inherently free. We just have different interpretations.
At the end of the day, I just thought the idea was cool, so I wanted to share it hoping someone might find it useful.