What does the etrex use??? I know how to set up my Garmin Map60Cx .. no idea for an etrex.
As for 'seeing the same things' on both .. is the etrex using OSM data?
Even if it is using OSM data what is chosen to be shown is up to the map maker.
Within OSMand there are various settings to show different things .. like road surfaces, bicycle routes .. and then different styles too.
So there too there will be different things shown depending on how it is set up.
And you can also use the different modes - car, bicycle and walking to show different things too.
Lots of variety here.
You remind me of an old Indian Railway joke.
Tourist wanted to find out want time a train left.
Asked when buying the ticket. Answer One.
Asked the platform attendant. Answer Two.
Sought the Station Master and asked again. Answer Three.
Then complained that he had 3 different answers at to when the train left. Station Master told him if he wanted the same answer then he should have asked the same person the same question.
Maybe you should look at only one of them?
I would start with a local paper map .. what coordinates does it have?
If you personally don't have or use a paper map .. chose the most popular maps that others use, probably OS - The National Grid OSGB36.
Then match those datum/coordinate systems on both etrex and OSMAnd ?
This makes it easier to obtain help .. both to and from others.