The two are different is the easiest way to say it. Streptococcus thermophilis is a probiotic strain that has nothing to do with the infection "strep".

There aren't any real good articles comparing the two that I can find quickly, but this makes the point:
"Streptococcus thermophilus has nothing to do with strep throat, which is caused by a completely different bug. These friendly bacteria are also used to make yogurts and cheeses, and they even assist Lactobacillus bulgaricus by making nutrients that assist with growth."
www.doctoroz.com/article/fact-sheet-probiotics