Hi KatyaS.
Your confusion must be greater than you realise yourself.
STMxxxxxx are STMicro products.
TI has nothing to do with that.
Most Arduino products are based on Atmel ARM technology, but there are different tastes.
There are even Intel based products.
I can understand one would like a single IDE to be used for different products, but how smart would it be to do that ?
You still need to take the chips possibilities in consideration, and how well would an IDE create code if it has to work well with all types of chips ?
I don't know whether there are extensions so the Arduino IDE will work with STM products, but such extensions do exist (You already found out about ESP and such).