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Plants that have xylem and phloem are vascular plants.
Non-vascular plants
Grass
mosses and liverworts
Echinodermata
Non-vascular plants (mosses and their relatives), Seedless vascular plants (ferns and their relatives), Gymnosperms (cone-bearing plants), and Angiosperms (flowering plants)
Non vascular plants consist of mosses, liverworts, and hornworts. They are normally found in moist places with a lot of rainfall.
Pteridophytes or Pteridophyta describes seedless, vascular plants that use spores to reproduce.
Primitive vascular plants are also know as a pteridophytes but fern is their more common name. The ferns life cycle is split between sporophytes phases and free-living gametophytes unlike other vascular plants.
Gymnosperms - 'naked seed'. But that does not include mosses, which are plants, but do not have true seeds. Ferns are vascular plants, but don't have seeds either.
Columbines have flowers and therefore seeds. They are vascular plants. The other names for this plant is Aquilegia, or granny's connet. The Latin name Aquilegia comes from the shape of the flower that looks like an eagle's claw.
Liverworts, hornworts, and moss are non-vascular plants. Another name for them is bryophyte. They do not produce flowers or seeds, instead they reproduce with spores.