Commensalism, mutualism, and parasitism are all different aspects of symbiosis. Symbiosis is latin for "live together". Animals tht live together are called symbionts so Allogalathea elegans and Galathea inflata and their host crinoids are symbionts. If the association is beneficial for both partners it is called mutualism. If only one partner benefits but the other is not harmed it's commensalism. When one partner benefits but the other is harmed it's parasitism. These aren't always absolute; it's more like a sliding scale with intermediate phases and shifts. for example, a shrimp that is normally a commensal may become a parasite if there is overcrowding or environmental stress & start feeding on the host's flesh. Or it may act as an mutualist if the host is infected by parasites or microbes and the shrimp acts as a cleaner & keeps the host in good health. Crab, shrimp, and even worm commensals will defend their hosts against predators in which case they're acting as mutualists. Then there's obligate and non-obligate symbionts and again different degrees of both. Generally speaking obligates cannot survive without their partners while non-obligates will mange. These crinoid galatheids can survive without their host but since their main feeding mode is taking plankton away from the crinoid they usually don't do as well without them.