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!