I can’t speak for anyone else, but I am incredibly competitive and that burns away the nerves once I’m actually in the ring. Things that make me nervous at home also make me nervous at shows, but my desire to win trumps the nerves.
I did a horse in a puissance-esqe type class this summer that got up to 1.4m before we dropped the rail to tie for the win. Had I just been schooling the horse, I would have never had any desire to take it higher than 1.15m. But I wanted to win, so we kept going (with owner’s blessing). I still get show nerves, but once I’m in the ring the competitive nature just takes over.