Are all prepaid SIM cards referred to as Tourist SIM cards in Thailand?
Nope. Just those targeting those that will be passing through for a couple of weeks. And those "tourist sim cards" are not exclusively for tourists, Thais can buy them also. But the English packaging and price is not targeting Thais.
...Or are there some prepaid SIM cards "for locals"?
Yes there are. You can get nearly any sim card available. Because promotions do change often, it is difficult to say which sim card to get.
But I can say from experience that a "local" sim card would usually be approximately ฿50-100 and then you layer on a plan on top of that. An exception would be for a specific plan like the 4Mbps unlimited internet for ฿600/6 months, ฿1200/12 months. I know someone who has a DTAC sim that is ฿200/mo for 60gb max speed internet and unlimited calls to all networks (15 minutes max per call). I think the sim card was 100 + first month. You have to keep your eyes peeled.
Another friend went to Hua Hin and got a new plan at a local shop. It was ฿50-100 for the SIM and then ฿200/month.
You go into either a branded True, AIS/Telewiz, Dtac, or a local shop with Oppo or other mobile phone branding (every Sub-district near the main wet market of that town has at least 1).