I'm not an expert, so this response is pretty crude. You may find
more info by searching the archives...

GPS altitude is the least precise of its measurements, primarily
because position is best determined by satellites on the horizon, and
altitude is best measured by satellites above (and if possible) below
your position. So it will vary more than position.

Pressure altitude is just that, a measurement of air pressure. In a
perfect world, you'd set the altimeter to 29.92, climb to 20,000' AGL,
then drop a line that's 20,000' long and it would just touch the
ground. But air isn't perfect so you have to adjust for temperature,
humidity, and whatever else to find out *precisely* how high you are.

Lucky for all of us flying types, we really don't need to do this as
long as we all use a decently calibrated altimeter and get a nearby
altimeter setting from a trusted source, such as AWOS. Now, all
aircraft in your vicinity are flying at the same, most likely,
incorrect physically, altitude, but it's all relative and as long as
all our altimeters indicate a different altitude, we don't bump into
each other.

This is the reason that using pure GPS altitude is a bad idea for
vertical navigation at the current time. Because not everyone has a
GPS altimeter, and because each receiver may come up with a different
solution for altitude, it's quite likely that two aircraft at
different indicated altitudes, could very likely be at the same
altitude.

I know this is very simplistic, but I think you get the point.

You *could* use GPS to measure an altitude gain, but you could NOT use
it to verify, for example, compliance with Class A airspace in the
USA.

-Tom