Alphabet, Abjad and so forth

[Michael]

We all know the term "alphabet", and there are probably quite
a few of us who are familiar with the term "abjad".

(Abjad is a term used to refer to a writing system -- like
the one used in Arabic -- that begins "a-b-j".)

Does English have any other terms that we use to refer to
a language's writing system should it fall outside of the
usual "abecedarian" approach ?

Thanks,
Michael