I am a little confused about this. Deception skill description says you oppose Discipline to it, but in opposed checks section it's stated you opposed Vigilance. What's the correct one?

Whichever feels most appropriate at the time.

Is the deceiver trying to convince someone that something they believe to be true isn't? I'd go with Discipline .

e.g. you're smuggling for Dak, who has been tipped off that you're skimming.

"Where's the spice?!"

"I made the delivery; if it's light it's your crew who's thieving!"

You roll Deceive, your difficulty is Dak's Discipline. You pass with an advantage - Dak remembers one of his men was acting real nervous when he asked them about this.

Is the deceiver trying to lie to someone who isn't sure of the facts ? I'd go with Vigilance .

e.g. an enforcer has been murdered; you're investigating it and are interviewing the usual suspects.

"What do you know?"

"Nothing; I wasn't even in the city last night."

GM rolls Deceive with your Vigilance as the difficulty. He fails with an advantage - the GM tells you he may not have been involved, but he definitely knows something.

Ask yourself, "Does the person you're lying to have their guard up?", "Have they made their mind up already?" and "Do they have information (of whatever accuracy) that will contradict what you're saying?" If the answer to 2 or 3 of these is "Yes", it's probably Discipline. Otherwise it's probably Vigilance.

Those are the two recommended skills but you can also use other skills if the situation makes sense. For example if a junk dealer is trying to cheat you by selling you a busted hyperdrive inverter thingy you could use Mechanics to catch the deception. The result would be slightly different as it wouldn't really tell if the dealer was knowingly trying to deceive you, he could just have been mistaken about the part's condition, but you'd still avoid buying the thingy. The same could go for a Knowledge based skill or almost any skill for that matter. The only thing is that if you use another skill you have to role play it as not necessarily catching them in a lie but catching an error and then extrapolating from there.

edit add:

These distinctions are valuable to good storytelling as it gives you more grey options on NPC interactions to play with, potentially making an encounter richer.

The opposite is also true, if you do use Discipline or Vigilance all a successful result tells you is that they are lying not the nature of the lie (though it may be obvious).

Another thought: Keep in mind that when you don't believe someone and start looking for a lie you are actually doing something. Your facial expression and body language changes subtly and your opponent may notice, and potentially react poorly (this would be a Threat result). However if you use another skill you're not trying to catch a deception but notice an error which if you do find or generate Threats will likely result in a different reaction. Being caught in "error" generally makes people less defensive than being caught in a lie.

I think most checks are a little flexible in what ability is used depending on the situation.

Kinda like how if you are picking a real key and tumbler lock you use Skullduggary, but if its an electronic lock you'd use Computers.

So really any skill could potentially be used to oppose deception. For example, say you are buying a used Speeder from a sleazy Toydarian. Instead of Discipline or Vigilance, maybe you'd use Mechanics or Piloting Planetary to see if he is deceiving you.

I see the rulebook as more like guidelines than actual rules. Most of the time you'll follow them, but other times you'll change them to fit the situation.