I think “babcia” is the literal term for “grandmother,” while “babushka” might be slang. I’m not 100% certain about that, but I do know that both terms are used in Polish families, depending on the family. “Babushka” was used within my family, and I know a few others of Polish descent who’ve used “babushka.” I also wonder if “babushka” is more common in some parts of Poland (i.e. those closer to Russia) than in others.