[ejplatzer]

Technically, a syllabary only refers to writing systems where the symbol represents the specific consonant and vowel pair, such as Japanese's Hiragana. For example, in a syllabary, the syllables "ka" and "ki" are two different symbols.

If the vowels are optional or not present, e.g. there's one "k" symbol regardless of the vowel, it's an Abjad. The archetypal Abjad is the Hebrew writing system.

If the vowels are written by adding them to the consonant symbol (similar to diacritics), it's called an Abugida. One example of this is the Ge'ez script in Ethiopia.

[Archelaos]

I did not want to make it too technical, so "Abjad" falls under "alphabets in the wider sense" and "Abugida" under "mixed forms". My comment was based on the assumption that the article in question does not necessarily refer to an alphabet in the strict sense. To make this clear, I did not think it was necessary to go into too much detail.