I've come across two different ways (at least, apparently for me) to classify verbs. Please note that this question is fundamentally different from Verb classifications by japanese learners.
The first classification is to divide verbs into Godan and Ichidan, which I think is good for reference, but not clear at all for learners (you can't really guess the number of conjugations by just looking at the verb).
The second, which I personally find clearer, is to divide them into る- and う-verbs. According to this last division:
With the exception of two verbs, all verbs fall into る- or う-verbs.
All る-verbs end in る, while う-verbs end in -う (including る). Therefore, if a verb does not end in る, it'll be necessarily a う.verb.
For verbs ending in る, if the vowel preceding る is /a/, /u/, /o/, it will always be an う-verb. If the vowel is /e/ or /i/, it will be a る-verb in most cases.
So what's the difference between the two? Is one system adopted by Japanese and the other adopted by learners (e.g. in JLPT)? Or they totally coincide but just have different names?