An impulse is five waves in the direction of the trend, a correction three against it. That is the main difference but not the only one: an impulse carries hard rules whose violation discards the markup, while corrections have fewer rules and more forms.
The impulse
Five legs numbered 1 to 5. Waves 1, 3 and 5 run with the trend; waves 2 and 4 are pullbacks against it.
The rules that must hold: wave 2 does not go beyond the start of wave 1, wave 4 does not enter wave 1's territory, and wave 3 must pass the end of wave 1. Markup breaking any one of them is discarded outright.
A separate variety is the diagonal, where waves 1 and 4 are allowed to overlap. It has its own rule in place of the suspended one, and its own write-up.
The correction
Three legs labelled A, B, C. There are several forms, distinguished by proportion:
Zigzag — the simplest three, where C travels noticeably further than A.
Flat — B returns almost to the start of A. It comes in running and expanded varieties, differing in how far B reaches and whether C exceeds the end of A.
Triangle — converging legs, each shorter than the last.
Combinations (WXY, WXYXZ) — several corrections in a row joined by connecting legs. This is the least determinate case: nothing says in advance how many corrections will end up joined together.
How to tell them apart
Not by appearance but by the proportions of the legs. A zigzag is recognised by C travelling further than A; a flat by B returning almost to the start of A; a triangle by its converging legs.
A useful marker is how far wave B reached. If it noticeably outgrew wave A, what you are looking at is probably not a correction of this degree but part of a larger move, and the count is worth checking one degree up.
Why this is not "bullish versus bearish"
An impulse is not the same as a rise. Five waves down is as much an impulse as five waves up; the trend simply points the other way. A correction in a downtrend runs upward.
The confusion comes from reading "impulse" as "a strong move up". In markup it is a term about structure, not about direction or strength.
What the distinction does not give you
Knowing that a correction is under way does not say when it will end or how. It says only how the stretch already travelled is built, and which forms the rules permit next.