How are plantlike protists classified into different groups

Protists are broken into three categories: plant-like, animal-like, and fungi-like. 
plant-like protists are photosynthetic, and tend to have flagella (tail-like structure for locomotion). Examples include red, green, and brown algae, as well as pryophyta and euglynophyta. 
animal-like protists are more amoeba like and include sporozoa. 
and fungi-like protists are only slime molds.