Interestingly - and I remember this from the days when my son was fascinated by construction sites and needed to know the words for everything - it would seem that Schauffelbagger is mainly used for toys. I think as a toy you would call this an excavator in English. Or maybe these words are just hyperonyms (Oberbegriffe).
If you want the terminologically correct words then you would use the following:
For the vehicle with wheels: Radlader - wheel loaderhttp://www.bildwoerterbuch.com/transport-und-fahrzeuge/schwermaschinen/radlader.php
backhoe is a part of the vehicle - Tieflöffel. The word can also be used to describe the whole vehicle. Another word is backhoe loader.
Löffelbagger - hydraulic shovel is apparently the "correcter" word for a Schauffelbagger. See here:http://www.bildwoerterbuch.com/transport-und-fahrzeuge/schwermaschinen/hydraulik-hochloeffelbagger.php
I thought I was finished with construction sites.....
Anyway, this took me down memory lane
, so thanks for that!!