Diffrences
plants have complex transportation systems (xylem) to transport water it goes from a source (water) to a sink (leaves) and algae doesn't have connective tissue instead all the cells absorb water directly from the source
plants have numerous ways to reproduce and such as forming seeds or asexually while algae tends to have more primitive and less numerous ways to reproduce.
plants are multi-cellular organisms while algae can be multi-cellular and uni-cellular or even colonial
they occupy different kingdoms plant: plantae and algae: protista
many algae can move through water via many mechanisms such as tails like flagella to swim through water
Similarities
both plants and algae tend to be non-locomotive they can both have root like structures to support themselves
they are both Eukaryota cells as they have cells with many components
they are both autotrophic (make their ow food) can both photosynthesise by the absorption of sunlight
they can both be found in many environment and in a large variety of biomes
hope that helps
