Prayer tends to imply (to a lot of people) that you are leaving the outcome up to some higher force, while "casting" makes it seem like you are the one affecting everything. To me they are ultimately the same, both connecting with a higher force to bring about what you want done. Casting just tends to be more assertive, more direct. I think that the whole "asking for permission" thing is part of the New Age magick movement, very concerned for the interests of others. If it is possible (i.e. you won't sound crazy or scare the person) to ask permission, by all means do so. Praying for someone I wouldn't say requires permission, because again, it's asking for the influence of a deity and is generally more "acceptable" in terms of supernatural influence in an event.
Sorry, kinda babbly -.-
In short: Prayer = no permission, Spell = get permission if you can and use your best judgement.