There is no difference in meaning between the two, though σταματάω is a little more colloquial. Basically, this verb and many others accented on the final omega are contracted verbs, and there are those which are contracted from -έω in Classical Greek (and these you can't conjugate in the other persons as -άς, ά[ει], -άμε, -άτε, -άν[ε], but -είς, -εί, -ούμε, -είτε, -ούν[ε]). The fact that you can open up σταματώ into σταματάω just shows you which endings you can use, in a way. Knowing these little facts can help when forming the simple future / subjunctive / imperative, and keeping in mind that the letter eta is a "long" vowel representing a bunch of vowels squashed together into one syllable explains why σταματάω gives σταματήσω but μπορώ (contracted form of μπο-ρέ-ω) gives μπορέσω. In Classical Greek (and Katharevousa) the future and subjunctive were formed by lengthening the vowels in the ending (ε + ε = η / ῃ, ο + ο = ω). Hope that helps and that I haven't confused you!

I'm not a native Greek speaker, but I do know the answer to your question. There's no difference in meaning between the two. However, one of them may be more common than the other. For example, the third person singular of the verb μιλάω/μιλώ could be either μιλάει or μιλά, but μιλάει seems to be much more common.

Thanks, gents!