On some site I was on months ago (I can't recall), it says that "очень приятно" is "nice to meet you" and I've heard a native Russian use that phrase. But, I've also used the Nemo app a bit and it says that "приятно познакомиться" is "nice to meet you" Are they the same? Does it matter? Is there a formality difference?
Yes, in a colloquial speech both forms are interchangeable,
очень приятно is just a shortened form for "очень приятно познакомиться" and it's completely acceptable to say whenever and whosever hand you shake the very first time.