What each one measures
An unweighted GPA treats every course as equal. An A is 4.0 whether it came from standard biology or from an AP course carrying a college-level workload, and the scale stops at 4.0 by definition. A weighted GPA adds a bonus to the harder courses, most commonly a full point for AP and IB and half a point for honours, which is how a transcript ends up reporting a 4.3 or a 4.6. Neither number is more correct than the other. They answer different questions: the unweighted figure asks how well you did, and the weighted figure asks how well you did against how much you took on. A transcript reporting only one of them is reporting half the picture, which is part of why admissions offices recalculate rather than read.
Why your school's weighting is not universal
There is no national standard for how much an AP course is worth, and schools genuinely differ. Some add a full point, some add half, some weight only certain subjects, and some do not weight at all. A few use a five-point or six-point scale that makes direct comparison meaningless unless you also know the scale. The practical consequence is that two students with identical coursework at different schools can carry weighted figures a full point apart, which is precisely the problem an admissions office has to solve. Most selective universities respond by recalculating from the course list itself, often stripping the bonus entirely, sometimes counting only academic subjects, and occasionally applying a bonus of their own. Your counsellor can tell you which formula your school uses; only the university can tell you which one it uses.
Which number to use, and when
Use the unweighted figure when comparing yourself against a published threshold, because most scholarship minimums, athletic eligibility rules, and stated admissions ranges are expressed on a four-point scale. Use the weighted figure when your school ranks on it, since class rank comes from whatever your school reports and that is the number deciding your position. Report both where an application gives you room, and say which scale each came from. The one situation where the distinction changes a decision is course selection: choosing between a likely A in a standard course and a likely B in an AP one, the weighted arithmetic often favours the harder course while the unweighted arithmetic never does. Work out both versions before you choose, rather than discovering the trade-off in June.