The basic answer:
Strava corrects the data form the Edge and this causes the difference
The more complex answer:
The Edge series ahas a few issues with altitude
The confounding factor is how the elevation is measured on the unit. This can be from the unit itself (barometer) the information in the GPS Signal or from the map data. Each will be different for different GPS units
The Edge series has a barometer and works on the fact that the barometric pressure changes with height, however it also changes with weather and temperature
Even before taking these into consideration, there is your start height.
Garmin recommends a manual setting of the barometer to a known height for each ride
So the data itself is only accurate to 10 feet at best, and then only if there is no change in weather or temperature. Under these circumstances it can be very inaccurate
Strava recognises this and "corrects" your unit's data accordinglly
The information on the Strava their
website is worth reading in full, butthe important poit is:
Strava detects devices with barometric altimeters and recognizes the data from that source. Since elevation data derived from a GPS signal is fairly inaccurate, Strava automatically corrects elevation derived from a GPS source by consulting elevation databases to determine the elevation at each point in the activity.
If you suspect that your elevation data is incorrect, you can request an elevation lookup.* Click on the "Elevation" text under the elevation statistic above the map. The dialogue pops up with a button to "Correct Elevation." This button will only appear for data collected with a Barometric Altimeter, or if a previous automatic elevation correction has failed. After a short while, the "Calculating" text will change to "Updated," and if you click on "Updated" your page will refresh with the new elevation data.
...and for a full discussion on elevation and Sports Devices as a whole see
this article on DC Rainmaker
Note: the article is dated and the Edge Touring Plus, 1000, 810, 800 and 510, all also contain a barometer