No, they both evolved from a common ancestor 1.5 billion years ago. Their common ancester likely lacked chlorophyll b and had a different light-harvesting system. Red algae got their distinctive color from phycoerythrin, which helps them absorb blue light in deeper waters. Green algae and land plants share chlorophyll, a key to their photosynthetic abilities.
Red algae thrive in deeper waters where blue light penetrates, while green algae dominate shallow waters because chlorophyll is much, much more efficient at absorbing red and blue light.
There are two other types too: brown and blue-green algae. Brown algae includes what some people call yellow algae, and large kelps that wash up on shore are brown algae. Blue-green algae isn’t actually algae! While we’ve agreed to call it that, it’s actually a photosynthetic bacteria.
The red-green algae split occurred about 200 million years after the broader separation of animals, plants, and fungi. Green algae later gave rise to land plants, with all land plants descending from green algae around 475 million years ago.
Both green algae and land plants share chlorophyll, a key to their photosynthetic abilities. Finally, green algae are generally considered the first true plants, while red algae remain classified as algae.