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Animal cells do not have cell walls or large central vacuoles to support their form. Animal cells do not have chloroplasts and are not autotrophs. They have mitochondria as organelles for cellular respiration. Animal cells store food as glycogen.
Animals have diplontic life cycles. This means the multicellular stage of the life cycle is diploid and the haploid stage has single celled gametes- like humans and other sexually reproducing animals.
Plant cells have walls and the central vacuole provide shape while turgid with water. They are autotrophs with chloroplasts for photosynthesis and mitochondria for cellular respiration.
Plant cells other than from mosses, hornworts or liverworts can form lignin and lignify ribbons of cellulose to reinforce cell walls. This both water proofs vascular tissue and makes the tissue able to support stems and trunks in plants no matter if the vacuole is turgid or not. This allows the use of dead mature cells to continue to provide trunk support to growing plants in the central dead wood.
No alga species produces lignin.
Charales, green algae ancestral to plants, have cell walls with cellulose and soluble pectins but non ancestral green Chlorophyta algae have agar or carageenin in cell walls. Red & brown algae have other cell wall materials. Coralline red algae has calcium carbonate in cell walls for structure.
Green algae have an alternation of generations in diploid 2n -> haploid 1n stages in their life cycle.
Green algae often have two or rarely four similar flagella when flagellate stages exist in the alternation of generations. Angiosperm and most gymnosperm species gametophyte stages produce gametes that lack flagella and only the ferns and moss retain flagellated gametes. This is why mosses and ferns remain tied to water for reproduction like the ancestral algae.
Alternation of generations in plants is a diplo-haplontic life cycle that alternates between spore producing sporophytes and gamete producing gametophytes. This means both spore and gamete producing stages are multicellular.
Algae are single celled or have colonial celled forms but none organize into true tissues that form organs.
Plants all store food reserves as starch in specialized cell organelles - plastids. Chloroplasts photosynthesize carbohydrates while leucoplasts store carbohydrates as starch. Chloroplasts use chorophyll a & b and carotenoids in the same ratio in green algae and in plants.
Red & brown algae use chlorophyll a but have other secondary pigments so they are different colors.
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