I would say that the spider is saprophitic and the starfish is holozoic.

why would you say the spider is saprophytic?

I guess it depends on what definitions one chooses. The term "saprophytic" is not used much anymore but generally refers to the ingestion of dead or decaying organic matter. By this definition, scavengers are saprophytes, which may be one of the reasons why the term is no longer commonly used. Spiders usually either secrete or inject digestive enzymes onto or into their prey and then suck up the digested organic matter. So saprophytic could apply to this mode of nutrition. Holozoic nutrition usually refers to the ingestion of solid organic matter, which spiders tend not to do. Some definitions of holozoic, though, include the ingestion of liquid organic matter, which would apply to spiders.

Well said. Saprophytic in this context could be rather misleading.

Biologists use the term "sea star" not starfish. It’s an Echinoderm people!