Is there is threshold between animals and plants?

The key characteristic that separates plants from animals is the capacity of plants to produce their own food with the use of light energy, h2o and co2 (photosynthesis). In your example, yes the sea anemone may look like a plant but ut has to rely on other organisms to live (heterotrophic) it feeds on particles and planktons that float along the body of water they are found in. :)