In actual use, AAVs often cannot integrate into the cellular genome. It's just used to temporarily deliver something else. In fact it's a commonly used vector for CRISPR/Cas systems.

But it's true that unmodified AAVs are capable of integration. It's a lot more specific about that than lentiviral vectors, because AAVs mostly just integrate into the human genome at the AAVS1 site.

Lentiviral vectors can insert at many, many sites throughout the genome. The same applies for transposon systems such as Sleeping Beauty and PiggyBac.

As for CRISPR/Cas, that's a whole range of systems that is mainly distinguished by the ability to easily program targeting of a specific sequence (in almost any context). That can be used to insert something at a specific genomic site, but it can also be used for all sorts of other things. Some Cas enzymes don't even target DNA but instead target RNA.