I think the confusion lies in that people seem to disassociate the two different types of Invokes because they are handled differently.
Think about it ... if you couldn't free tag an Invoke for Effect, it would mean that you'd need to spend a Fate point to pick your own weapon off the ground
Mind you, I was always under the impression that Invokes, even Invokes for Effect, were something that benefited you and that doing something that negatively affected someone else fell under the realm of a Compel. Imma thinking I need to reread the Compel section again.
Later Edit: Nevermind, this has been answered. They are different things, but one can cause the other: "A tag is an invoke (tag just means free invoke); an invoke can be done as an invoke for effect; an invoke triggers a compel, which is run between the GM and the target."