urge= insist, implore

encourage=gently coax

urge is a stronger, more forceful term - more urgent in fact

encourage may often be used in combination with adverbs such as 'gently' or 'mildly'

This is by no means an exhaustive account of the differences just those that first came to mind

I think in your particualr context, there probably isn't really any difference; I think the writer is probably just using the different words for variety.

I don't honestly think there is a huge difference between the "strength" of the two words, either — any such difference mainly arises from the way in which they are being used. Certainly, here, from the way the questions are worded, I don't think the writer is making any particular distinction of one being 'stronger' than the other.

HOWEVER, where I would identify a difference (but which I don't believe is applicable here) is in the implications behind the two words. Although a very long way from being a hard-and-fast rule, I think one might say that in the most general of ways, you are more likely to "urge" something to do something they don"t want to do, and to "encourage" someone in doing something they maybe do already want to do.

NS OED:
urge
2 v.t. Advocate or recommend (a course of action, that, etc.) eagerly or insistently.
3 v.t. Entreat earnestly or persistently (to do); incite or impel strongly.

encourage
1 Give courage, confidence, or hope to.
2 Make sufficiently confident or bold to do a specified action.
3 Urge, incite; recommend, advise.