I think prissygirl is right, we have a proper classification system of plants.
Firstly A plant is an organism in the kingdom Plantae. According to the five-kingdom classification system used by most biologists, plants have the following characteristics: they are multicellular during part of their life; they are eukaryotic, in that their cells have nuclei; they reproduce sexually; they have chloroplasts with chlorophyll-a, chlorophyll-b and carotenoids as photosynthetic pigments; they have cell walls with cellulose, a complex carbohydrate; they have life cycles with an alternation of a sporophyte phase and a gametophyte phase; they develop organs which become specialized for photosynthesis, reproduction, or mineral uptake; and most live on land during their life cycle.
Biologists have identified about 500,000 species of plants, although there are many undiscovered species in the tropics.

Common Classification

Plants are classified into these groups :

Algae
Bryophytes
Pteridophytes
Gymnosperms
Angiosperms

There are a few other higher categories of classification you may come across in your reading.

Lower plants usually include algae and Bryophytes, while higher plants refer to Pteridophytes, Gymnosperms and Angiosperms.

The word Cryptogams literally means "hidden wedding" and alludes to the fact that the sex life of these plants (algae, Bryophytes and Pteridophytes) was once not understood. Phanerogams ("open wedding") are the seed plants - the gymnosperms and angiosperms.

Thallophytes is an outmoded term for plants whose body is not differentiated into root/stem/leaves but is termed a thallus. Algae fall into this category (and fungi did too when they were considered to be plants).

Vascular plants are those with vascular tissue (xylem & phloem). Embryophytes (all but algae) are plants that bear an embryo and are synonymous with land plants.

I think your confusion might be over now.