The other main kind of verb is the う verb. The real difference between irregular, る, and う verbs is that they are conjugated differently.
For う verbs, the verbs all end in the う sound. Unlike る verbs where they just ended with る, う verbs end in all other う sounds (く, す, つ, む, ぬ, etc.) INCLUDING る.
Recall that for る verbs, the sound before it was either an い or え sound (i.e. たべる taBERU, おきる oKIRU). For う verbs, it can be any sound. That includes い or え sounds also, making it more confusing!
What does this all mean though? If a verb ends in -ある, うる, or おる, it IS an う verb. If a verb ends in いる or える, it is EITHER a る or う verb. The only way of telling is if you recognize one of its conjugations to distinguish it as る or う, or if you just know what kind of verb it is. Let me give you an example:
かえる (kaeru) - to return
はしる (hashiru) - to run
They both end in いる and える, so that makes them る verbs right? If you were to conjugate these into their -masu forms (drop the る, add -ます), they turn into:
However, this is INCORRECT! It's because these two verbs are う verbs! Their correct -masu forms would be かえります (kaerimasu) and はしります (hashirimasu), respectively. The point here is that if a verb ends in る (even if the sound before it is an い or え sound), it doesn't necessarily make it a る verb! I know this sounds confusing, but you'll eventually learn different conjugations and be able to tell which verbs are る or う.
Here are some examples of う verbs so you can get a sense of what they look like:
かく (kaku) - to write
よむ (yomu) - to read
はなす (hanasu) - to speak
たつ (tatsu) - to stand
うる (uru) - to sell
あそぶ (asobu) - to play
As you can see, う verbs are much more diverse in the sense that they have more variety in the ending sounds, like -aku in かく (kAKU) and -obu in あそぶ (asOBU).
I know that う verbs seem difficult, but as you learn more and more Japanese you'll learn to tell う and る verbs apart. It'll also be important to recognize the difference too when it comes to seeing conjugated forms so you can work backwards and figure out what the verb actually is. Of course though, this all takes practice, so study hard!