Verified answer

first of all, first sentence must be like "Elena ide"t k zele"nym poljam" ;)

and yes, there is a bit difference. Since Russian has no Continuous or Perfect Tenses, we use perfect and imperfect verbs instead. Verbs without any prefixes are always imperfect, so "idti" is imperfect verb (it starts with 'root' from the very beginning). so, first sentence means "Hellen IS GOING to green fields (she is on her way somewhere)".

"podhodit'" is perfect verb (it contains prefix 'pod-', which means almost completed action in this case), so the second sentence means "Hellen APPROACHES the green fields (and she is almost there at the moment)"

p.s. it is possible to make imperfect verb from the verb with prefix, that means that "verbs without any prefixes are always imperfect", but opposite isn't correct.

Hope it helps!