Hmm, they have pretty different meanings IMO :).
초대하다 refers to "to invite" when (요)청하다 is "to request, to ask for (often used in formal occasions, though)."
(요청하다 = 청하다. 요청하다 is more commonly used :))
*초대하다
나의 생일 파티에 친구를 초대했다
=I *invited my friends to my birthday party.
*(요)청하다
정부가 도움을 요청했습니다.
=The government asked for help.
Hope that helps :)!