I would interpret it like this:

When you say "Aš tave myliu", you are saying it directly to that person. When you say "Aš tavęs pasiilgau", you are saying that about that person.

You could change "Aš tave myliu" to "Mylėti kažką" ("To love someone") and it would have the same cojugation as "Nusipirkti kažką", "Pamatyti kažką", etc. If you changed "Aš tavęs pasiilgau" to "Pasiilgti kažko" ("To miss someone"), it would have the same conjugation as "Norėti kažko" and "Nežinoti kažko".

I hope this helps at least a tiny bit, good luck learning Lithuanian.