This depends on how far back in time your text is about. If its Hornblower stuff the captain was the ship's captain aided by his lieutenants (today's 'styrmän). Styrman was what the title say: the man at the tiller, in other words the 'helmsman'. This title changed only when the tiller was abandoned in favour of a wheel on quater deck (quartermaster). The mates were sailors under one of the professionals like carpenter's mate, bosuns mate etc. and served in the capacity of assistants or companion. And at least the Brittish kept those titles as along as the tall ships commanded the seas.