https://doi.org/10.1351/goldbook.A00268
Cations formally derived by the addition of one hydron to the $\ce{N}$ or $\ce{O}$ atom of an amide and $N$-hydrocarbyl derivatives thereof. In organic chemistry an unspecified amidium ion is commonly a carboxamidium ion
or
The term does not imply knowledge concerning the position of the cationic centre, e.g. $\ce{PhC(=O)N^{+}Me3}$ N,N,N-trimethylbenzamidium.

