I think it'd be fair to say (although a gross oversimplification) that Bluegrass emphasizes the "individual" -- every performer expects to "take a break" and showcase him- or herself in a solo in every number, to the point of being competitive even with fellow band members. Old Time is more of a "collective" style -- often there are no solos, and an instrumental break will consist of everybody playing the melody at once.

As for the "Celtic" aspect, many of the settlers of Appalachia were Scots-Irish (Protestants descended from the Scots who had been transplanted into Northern Ireland, England's first colony) and brought both Scottish and Irish songs and tunes with them to America. Later admixtures of black and Eutopean musics were added. (The banjo came from Africa, the guitar from Spain.) This too is a gross oversimplification, but Celtic is one ancestor of Old Time, which was the main ancestor of Bluegrass.