The Japanese language has two types of regular verbs that involve the stem, and can be referred to as Japanese consonant and vowel verbs.
The two groups of verbs are:
Most verbs are consonant-stem, but vowel-stem verbs are also common, hence the numbering "Group I" (consonant-stem, more common) and "Group II" (vowel-stem, less common). Sometimes categorization is expanded to include "Group III" (special cases) for the irregular verbs する suru and 来る kuru; note however that there are other Japanese irregular verbs, though they are generally only slightly irregular.
Consonant-stem verbs end in -u (-au, -iu, -uu, -ou), -ku, -gu, -su, -tsu, -nu, -bu, -mu or -ru, but not -eu, -zu, -dzu, -fu, -pu, or the defective columns -yu or -wu.
All vowel-stem verbs end in either -iru or -eru. However, not all verbs ending in -iru or -eru are vowel-stem verbs; for example, hashiru, "run", is a consonant-stem verb. Verbs ending in -aru, -uru and -oru also exist, and are all consonant-stem.
The Japanese names ("5-class" and "1-class") are based on the number of vowel suffixes used to form verb roots for conjugations. Classical Japanese had more verb groups (such as 2-class and 4-class) which are archaic in Modern Japanese.
Consonant-stem verbs conjugate differently from the vowel-stem verbs. Consonant-stem verbs conjugate after a consonant, and vowel-stem verbs conjugate after a vowel, as can be seen in the following examples:
Consonant-stem verbs ending in -u (-au, -iu and -ou) may not appear to conjugate "after a consonant"; for example, the polite form of kau (買う, "buy") is kaimasu (ka.u → ka.imasu). However, the stem is in these cases technically considered to end in the consonant w. The w is normally suppressed, but surfaces in the negative form, as in kaw.anai ("does not buy"). Traditionally these verbs ended in -hu, which is still seen on occasion in historical kana usage, and thus unambiguously ended in h.
The terms "consonant-stem" and "vowel-stem" come from considering the invariant part of the verb (the verb stem) on the basis of phonemes – concretely, by writing in rōmaji. This is an abstract perspective, as the consonant stem itself never occurs independently, but only with a following vowel, as Japanese words are formed of morae – concretely, writing in kana. For example, while the stem of yomu is yom-, the bare *yom is not an independent word.