Predation and parasitism are similar because in both predation and parasitism -

Responses

both organisms are harmed in some way
both organisms are harmed in some way, EndFragment,

both organisms receive a benefit
both organisms receive a benefit, EndFragment,

one organism is harmed while the other benefits
one organism is harmed while the other benefits, EndFragment,

one organism is neither harmed nor benefits
one organism is neither harmed nor benefits, EndFragment,

one organism is harmed while the other benefits.

In predation, one organism (the predator) hunts and consumes another organism (the prey) for nutrition, while in parasitism, one organism (the parasite) lives off of another organism (the host) without immediately killing it. In both cases, one organism benefits while the other is harmed.