Cell Wall
All plants and most algae have cell walls. The cell wall is a flexible layer outside the cell membrane that provides structural support to the cell. The wall is permeable to allow for some nutrients to pass in and out of the cell. Unlike algae and plants, protists and animals do not have cell walls.
Photosynthesis
The cells of algae and plants both contain chloroplasts. Chloroplasts capture light and turn it into energy in a process known as photosynthesis. Chloroplasts are pigmented with green chlorophyll, which is why so many plants and algae are green. Organisms that use photosynthesis are called autotrophs, which means that they provide nutrients for themselves rather than feeding on other organisms.
Eukaryotic Cells
Plants and algae, as well as animals, have eukaryotic cells. The primary difference between eukaryotic cells and prokaryotic cells -- like those of bacteria -- is that eukaryotes have a nucleus within the cell.
Genetics and Reproduction
Because both plants and algae are eukaryotes, most of their genetic material is housed in the cell's nucleus. Both types of cells have DNA and similar amino acid sequences. They can reproduce through cellular division. When a cell is ready to divide, it forms a cell plate. The DNA and cells then split in half to create a new cell.
Differences
A few important differences distinguish plants from algae. Most algae are unicellular, while most plants -- except for the tiniest -- are multicellular. Algae also lack the complex root, stem and leaf structure of plants.