Daniels:

abjad a type of writing system that denotes only consonants

The Unicode Standard:

Abjad. A consonant writing system. The main letters are all
consonants (or long vowels) with other vowels either left out
entirely or indicated with secondary marking of the consonants. The
best-known example is the Arabic writing system, and the term "abjad"
is derived from the first four letters of the traditional order of
the Arabic script.

Daniels commented:

>The differences, for the one among you who cannot see them: absense of
>"only"; presence of "(or long vowels)"; mention of secondary markings;
>bad example. The only pure example is Phoenician.

So, given this, one might propose the following revision:

Abjad. A writing system in which only consonants are indicated. A
well-known example is the Arabic writing system, though it is not a
"pure" abjad because consonant letters like /w/ and /y/ are used to
mark long vowels /o/ or /u/ or /i/. In some abjads, vowels can also
be indicated by the use of secondary marks on the consonants. The
term "abjad" is derived from the first four letters of the
traditional order of the Arabic script.

I believe that this is accurate. Comment is invited. And yes, I am
leaving Abugida for the last.
Michael Everson * * Everson Typography * * http://www.evertype.com