Knowledge is always advancing and there’s been a revolution in classification over the last 20 years. Odds are your school was using an older model.

Currently the standard model is something like Plantae (true plants) and Algae (marine plants) are part of Viridiplantae (green plants) in the kingdom of Archaeoplastida or Plantaesensulato (plants in the broad sense). But some scientist prefer to use Plantae in place of Viridiplantae and/or Archaeoplastida. Basically plant as a colloquial term is used both for the kingdom, and for a specific clade, and a specific subclade. So kelp is a plant in the sense of kingdom, and clade, but not a plant in the sense that it doesn’t belong to the sub-clade of true plants.

But don’t memorize that yet, because it’s actively being argued about and it’s likely definitions will change often over the next 20 years.