Richard Bridge well said,there is also an ambiguous chord[strictly speaking dyad]which contains the note b and d,5 string second fret,3 string 4th fret,this can be used for either b minor or g major,but probably works better when there is a b or d in the melody,the rerason this works is that both gmajor and b minor contain the notes b and d,if you want to use any tuning successfully[imo],it is necessary to understand what you are doing and all the different inversions available to you.
d7 chord,2 string ist fret,3 string second fret,can be moved up two frets,for a top four string e7,this time your inversion,is trebling the seventh note the d,and you have no e note,if you want the e note,play 1 string or 4string or both, second fret,with your shape.Dick Miles