Untap vs Next Untap

Some VTES cards list "During your untap phase..." and some list "During your next untap phase..."

A player in our group is using Psychic Projection as an example that sometimes it's your next untap phase sometimes it's the untap phase AFTER the next.

If you look at the Psychic Projection example above, basic lists "Burn this card during your untap phase", where superior says "Burn this card during your next untap phase".

So, question is - if a card lists something as "During your next untap phase", does that really mean it's the untap phase AFTER the next?

Another example would be Sensory Overload - does this stay around for a full round (burn on your 2nd untap phase after played)?

For Psychic Projection, there is no difference in those two burn clauses, they both appear on your next untap phase, for Sensory Overload however, there is a very important difference between the basic and superior. The main thing here is that you still control Sensory Overload even though it goes (usually) on someone elses minion. Like say you play it on your preys vampire, at basic it would burn at the end of your preys turn, but at superior it wont burn until the start of your next turn, which is quite different thing.

That last part would be moot anyway Ankha, since untapping cards is the very first thing you do during your untap phase before you can do any 'during untap phase' effects.

For psychic projection, is there a reason why the superior version says "next untap phase"? I'm trying to figure out why the distinction is made. Is the "next" really necessary?