The short answer is that you NEED to know the carrier to send an SMS (or email) message from the computer.

Phone carriers exchange gateway and list information with each other, so sending a text message from one carrier to another is handled internally using dedicated gateways from one carrier to another. But if you were say, making a paging system and want to text cell phones when a job is complete. (or a file system fills up), then both the email and SMS gateways will require you to know the carrier. I know that where I work, they ask for the phone number and carrier and then that determines the message delivery. Sometimes it's SMS, sometimes email. It all depends on who has a public gateway and what it is.