Oh, that's the other difference. Bigger one I guess. In the ocean, all kinds of phyto are there at a low concentration. You would need a large culture, on the order of ocean sized, to feed like that. In the culture, you want one species of phyto at a time. And you want to grow them to a ridiculous concentration, green water. You will need a concentration of nutrients way above what is in the ocean. You might or might not get that from detritus from your tank.
What will definitely come with detritus is other living stuff. Mostly bacteria. They will compete for nutrients in your phyto culture. They may or may not crash the culture, but you won't get an optimal culture.