As you know, spellcraft can be used to determine what spell was cast. Of course, if no somatic or verbal components are present, a spellcraft check can only be used if you roll a save against the spell or if the effects of the spell are visible. However, we run into a problem: Spells with similar effects. I wish to expound upon this.
For conjuration (teleportation) spells, the effects from spell to spell vary, but only so far as the destination might be closer or further away. If you don’t see the destination the person arrived in, you really haven’t seen the total effect of the spell, so how do you know what spell was cast? Was it a plane shift, greater plane shift, teleport, greater teleport, or perhaps just a dimension door? In these cases, it is impossible to determine exactly what spell was cast, provided that there were no vocal or somatic components, as well as no visible focus or material component (such as with plane shift), the spell was not cast on you (thus allowing you a saving throw) and you cannot see the destination of the teleportation effect. Spell-like abilities which do not have the majority of these provisions are even more difficult to determine. A sleight of hand check may be made to pull out a material component without your opponent noticing the material component. However, with spellcraft you can determine that it was in fact a teleportation spell, thus you wouldn’t confuse it with, say, an invisibility spell. However, there is still one thing you can use to help you determine which spell might have been used: Detect magic. This spell gives you roughly the power level of the lingering aura. I am aware that lingering auras do not give you the power level, however for this campaign setting for conjuration (teleportation) I will allow this use of detect magic.
For spells that produce an Invisibility effect, such as invisibility, greater invisibility or superior invisibility, the same problem occurs. A creature becomes invisible, however you aren’t observing the full effect of the spell without certain provisions. In these cases, it is impossible to determine exactly what spell was cast, provided that there were no vocal or somatic components, as well as no visible focus or material component (such as with invisibility), the spell was not cast on you (thus allowing a saving throw). Spell-like abilities which do not have the majority of these provisions are even more difficult to determine, though you can still tell with spellcraft that they’re invisible. There are ways to tell, however. With an invisibility spell, you can tell they vanished, but it isn’t until they become visible again after making an offensive move that the spell was clearly the invisibility spell. With greater invisibility, it becomes obvious when you feel a sharp point in your side after the man holding the dagger went invisible and is still visible even after attack. With both of these cases, see invisibility will pierce the illusion, ruling out Superior Invisibility. Now, Superior Invisibility is only obvious when they don’t appear after an attack and also that you cannot hear them either. If they’re moving silently it would be impossible to tell whether they’re Superior in their Invisibility or just really sneaky. However, casting see invisibility and still not being able to see them However, you are entitled to use spellcraft to determine that this is a Superior Invisibility spell and you should use True Seeing spell instead.
In either case, you can also use detect magic as stated above with teleportation spells to determine the relative power level of the lingering aura. If it was a faint lingering aura, it was probably invisibility. If it was a moderate aura, it was probably greater invisibility, and if it was a strong aura it was probably Superior Invisibility.
In short, you are not witnessing the full effects of the spells above provided they lack somatic, verbal, material and focal components or are spell-like abilities, and thus cannot determine precisely what spell it was, however you are witnessing some of the effects and thus can tell the difference between invisibility and teleportation. You can use detect magic to give yourself a better idea of what happened.