Hi

no, algae are algae

In terms of evolution, you could say algae are ancestors of land plant because they have certain features that are advanced in land plant. Algae are not really plant, but they share an evolutionary link with land plant, as they can both photosythesize and have other features that are advnaced in plants like I said earlier. Overall, Algae are not plant. They are ancestors of plant.

Protist

Only some algae could be considered "plants". They are not the plants we usually refer to as those we call terrestrial plants. But you can refer to the clade Viridiplantae as plants since they share a common ancestor with primary chloroplasts. Only red algae, Glaucophyta (a small group of unicellular algae) and green algae (comprised by two separate but sister groups: Chlorophyta and Charophyta, the latter of which is the one that has land plants inside of it). So plants come from green algae that started to move from aquatic habitats to land, eventually becoming what we know today. Although in the end these are just names and you could very well call all these related groups "plants" or it would be more accurate to think of plants as a kind of green algae that has evolved a lot. Similar to how birds in the end are just a different kind of reptile that us, humans, consider different enough as to have a special name. We are the ones who decide what is a plant anf and what isn't.