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.
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.