A specific prophecy (or word of knowledge) would, by definition, be more specific. If you need an example, let's just start with something simple like someone prophesies that you'll get into a car accident. If tomorrow you're not in said car accident, well, you know the prophecy was false. If it happens, sure, suppose it was just coincidence. But, let's further suppose the person making the prophecy prophesies this several times, and every time it comes true. The degree of certainty is increased as the probability of multiple coincidences happening without error goes down.
Further, let's assume this event really rattles you, and so you decide to go into a church. As you enter the building, someone is prophesying that someone named Jason was in a car accident today, and was struck by a driver in a white Chevy pickup. The person then goes on to say that Jason has also been committing adultery and cheated the government this past year by $2500 on his taxes. At this point, the prophecies would clearly be getting more specific. Sure, could all totally still be "coincidence", but that probability is now effectively approaching zero if all that is said is indeed accurate.
I think we saw this a lot in 2012 as the "end of the world" prophecies we're all claiming days and times when the world would end. Since clearly the world did not end on those dates, we can conclude those were false prophecies. I wouldn't even claim them as "vague" prophecies that are open ended, they were clearly just "false" since they made a claim which included and event and a timeline, and the timelines expired without events taking place. Clearly, as presented, these are false "specific" prophecies, not vague predictions. The Bible itself warns that "prophets" are vetted simply by whether the prophecies come true or not. One who prophesies false events is, by definition, a false prophet and should be rejected.