I read that moving tokens onto a card that can be advanced (like Trick of Light) is different from advancing an actual card.

So if I use trick of light to move 2 tokens onto an advanceable card that has zero advancements, is it still at zero? Do I pay 2 clicks and credits to advance it 2 times, simply keeping the tokens on the card?

No. It now has two advancement tokens and so counts as having been advanced twice. Pack another click and pay a credit to put on another token and it has been advanced 3 times.

I think the difference is between "put an advancement token on a card" (or something similar) and "advance a card". You can only "advance" cards which say they can be advanced (so only agendas, advanceable ice and assets that say they can be advanced, like most of the nastier traps). However, if a card just lets you put a token on another card, it doesn't need to be able to be advanced to allow you to do that (so you could put it on Snare! for example).

Trick of Light specifically mentions you can only move them to cards that can be advanced, so it still has that limitation, but the upcoming Jinteki identity does not (if I have understood correctly), as it just specifies a "card".

In addition to what borithan said there are a couple of other times where the difference is important. For instance efficiency committee says that once you use the token you can't advance cards anymore however you can still place advancment tokens on cards even after you've used efficiency committee using Shipment from SanSan or Shipment from Kaguya etc...

Yeah, I think frybender's distinction is the most important one. Nothing in the game (at present) can stop you 'placing' or 'moving' an advancement token; however certain effects (most notably efficiency committee) can prevent you from 'advancing a card'.

There are some crazy combos you can pull off with HB: Cerebral Imaging where you can get 7 AP in one turn using this fact, but they require luck and set-up time.

Thank you for the answers guys!

I have another quick question that I didn't want to start a new thread for...

When corp retrieves a card from his archives, and it's a face up card, does he have to show the runner which card he retrieved?

Edit: NVM I found the answer. Runner is allowed to see which card is retrieved.