Algae and plants may look similar and belong to the same Eukarya domain, they don't belong to the same kingdom because they are simply different in many ways including in their behavior, structure and habitat. In totality, they differ in more ways than they are alike.
Plants are in the Kingdom Plantae, while Algae are in the Protista kingdom. Plants are multicellular, while most Algae are single-celled, although some can be multi-cellular.