What you learned is correct.
However, in everyday conversation or informal chatty writing, people aren't as precise as the grammar books, and it's possible that someone might use the first sentence even if someone else was going to cut their hair. It's the sort of thing that happens.
The converse seems less likely though. I can't really imagine anyone saying "getting my hair cut" if they were planning to cut it themselves.
You asked for comments on your writing:
From what I learned from ["from" is not wrong, but "in" would IMO be better here, if only to avoid repetition of "from"] my English grammar class, the first sentence is not quite right unless you actually cut are actually going to cut your hair by yourself. But I saw have seen in quite a few cases that the first expression - not exactly the same, rather of that sort - are is used meaning the to mean the same as the second sentence. Is this something that is grammartically grammatically incorrect but used often, or is it just plain wrong?
Thanks in advance... one more thing... if you found ["found" is not wrong, but "find" seems better to me] any errors in my writing above, please correct me. It would be greatly appreciated.