While a vegetarian diet typically eschews meat, chicken, and fish, there are varying degrees of vegetarianism. Vegetarian diets range from veganism, which abstains from all animal products (for some, even forgoing honey), to diets that include eggs or dairy products, or both (via Healthline). Since protein sources are limited, a vegetarian diet include legumes and grains, as well as breads and pasta in addition to a rainbow of vegetables and fruits, which makes it higher carb (via WebMD).
Some people follow a vegetarian diet for ethical or environmental reasons, however there are proven health benefits. By eliminating meat, dietary intake of saturated fat lowers while vitamins, minerals, folic acid, and phytochemicals increase, which lowers bad cholesterol and blood pressure (via Harvard Health Publishing). Plant-based diets may even lower you risk of developing certain cancers.
While the two diets seem to be opposites, you can actually be both keto and vegetarian. Diet Doctor explains that by lowering carb intake to 20 grams per day and incorporating higher fat proteins like eggs and Greek yogurt as well as cheeses and nut butters, it is possible to have the health benefits of both diets. While being keto and vegan is possible, the vegan diet relies heavily on higher carb grains and legumes for protein intake, which makes keto harder to follow.
So, while keto-followers may not be able to have vegan cake, they can still enjoy some keto ganache.