Not quite. Once an Aspect is applied or discovered, the person who applied/discovered it may tag it for free or pass the tag along to someone else. If the Aspect is fragile, it goes away after the tag. If it's sticky, it hangs around, but further uses of it are invokes, not tags. You can only tag an Aspect once, regardless of how long it lasts.
Okay, now I get it. I thought that Invoke just meant your own Aspects, while Tag meant basically invoking Aspects that belonged (however they got them) to others, or the scene. So just to clarify, Tagging is free, but only if you applied or discovered the Aspect, or if you pass the tag to another, and only once, while Invoking always costs Fate, and can be used while you have Fate and the Aspect is present?
Sorry, still new to the Fate system.