If I asked you to draw me an amide, we'd likely end up with something in the form of:
The exact definition of this is given fairly clearly in the IUPAC gold book.
Derivatives of oxoacids [...] in which an acidic hydroxy group has been replaced by an amino or substituted amino group. Chalcogen replacement analogues are called thio-, seleno- and telluro-amides. Compounds having one, two or three acyl groups on a given nitrogen are generically included and may be designated as primary, secondary and tertiary amides, respectively Source: IUPAC Gold Book, 1995 recommendations
There is however another class of compounds which we call 'amides', for instance LDA (lithium diisopropylamide). Again, the IUPAC gold book has this covered.
The term applies also to metal derivatives of ammonia and amines, in which a cation replaces a hydrogen atom on nitrogen.
I fully accept this, my question is, why we decided to re-use the word 'amide' to describe these compounds. Is the reason historical (i.e. before we knew better), or is there a logical basis for the grouping of the two classes of compounds.