They need calibrating, like any barometric gauge. You have to find the actual elevation at a reference point and you set that as a location in the Garmin when you are at that point.
https://support.garmin.com/support/searchSupport/case.faces?caseId=%7Bdf7142e0-ea50-11e0-73d0-000000000000%7D
That “older” Garmin – how old? Does it have a barometer at all? If not, it will be reading GPS altitude and that will be way off.
Yes you can get the web sites to “correct” it, though that’s based on topographical elevation for the GPS position. That data may not have a fine resolution so the elevation may be generalised for a 100m square (for example) and thus not be right either unless that whole area is flat. Though when comparing against others it’s at least more consistent.