Yes, the elevation is based on sea level. I don't fly much and recently landed in Denver and was watching the altitude on the screen in front of me. As we were descending we landed well before I was thinking we would, about a mile in elevation above sea level.. it was "duh" obvious when it happened, but I was tired and clearly not thinking about it!

And using the ground proximity to guide a landing instead of altitude has lead to some crashes I have read.

This only holds true if you’re flying at or above the transition altitude. The transition altitude depends on where you’re flying: for example, in the USA and Canada it’s 18_000 feet MSL.

The plane is measuring altitude, which is relative to a reference point, unlike elevation which is relative to sea level. And if the altitude is determined by pressure sensor, musn't it be relative to the ground directly below the plane, anyway?

(Although personally, I agree with the sibling comment that the variability is likely an artifact of the sensor resolution.)