Elevation totals are always an approximation.
I just assume it's within 10% or so, and that's good enough.
Barometers
These can be affected by changes in the weather. I got 200 feet of elevation gain at a rest stop when a tiny thunderstorm rolled through (lowering the air pressure). And it can be affected by the bike wind speed.
But I can walk upstairs with my Garmin and watch it count off elevation feet as I climb. Just think of the tiny difference in air pressure in a couple of stair steps! That's amazing to me.
EDIT -- I've been on the Blue Ridge Parkway, and the overlooks have signs showing the elevation there. I'm often within 25 feet or less of the number. That's very good.
GPS elevation
It's fast for GPS devices to locate your spot on the ground, since the satellites are located at lots of different directions. It calculates the intersection of circles (spheres) from each satellite, and the satelllite position is known to high precision.
But elevation takes longer to get an accurate number. On my old Garmin 705, it has an "averaging" option when saving a location, and I can see the elevation number converge to an accurate value, but it takes 30 seconds to a minute, averaging in new readings ever second. On my newer phone, the GPS elevation calculation is faster, more like 10 to 20 seconds. But these are too slow to do continuously while riding.
Using mapped elevations
There are known elevation points on the maps, and the roads nearby are calculated from these points. If the road is heading up on the side of a mountain, the software needs to estimate exactly where the road is, and can be off a few feet. Bridges often show as a dip down to the river level and back up again.
Rounding and smoothing
It's a complicated problem. Here's the ridewithgps programmer, Cullen King's blog, on
elevation calculations. Lots of math to correct the raw data.
I posted a comment about smoothing my Garmin 705 recordings in
this post. It includes some graphs showing the smoothing changes.
Years ago, back when I still used mapmyride, they ignored any small elevation of 10 meters/33 feet. I can see the argument for this, but it makes a lot of rides with small rolling hills show up very flat.