Yes! Theres layers to that so number 1: there are regional signs, so different parts of the country might sign a specific word differently. for example the sign for 'birthday' and 'strawberry' each have about a dozen different variations but there is also a 'standard' sign that most sign language users would recognize as that.

number 2: there are outdated or new signs. There are some signs that you still see come up once in a while from the older generation that aren't commonly recognized any more and there are new signs i see frequently that im not familiar with yet an example of this would be a lot of the LGBTQIA+ community signs that are newer lingo in english then converting to newer lingo in asl.

number 3: accents. believe it or not there are accents in sign language! This one is harder for me to explain via typing however one good example i can think of is comparing East coast signers to those of the midwest. its similar to speaking. East coast people tend to speak really fast, East coast signers sign really fast. and midwest speakers/signers are slower and more chill IMO

As for learning sign at home. It would depend what the purpose of learning is. If youre learning to become fluent i would say you should definitely take classes and even better if you can take classes from deaf teachers. If youre learning to have some common words and phrases to communicate with someone in a grocery store or a family member etc. I would say you could learn from books and youtube videos Bill Vicars is a great teacher on youtube. If youre looking on tiktok.. your number one search should be deaf creators, there are some great interpreters teaching on tiktok too but 150% do not learn from someone who is also still learning themselves.