A vegan diet is easily defined. It does not include any animal derived food products what so ever.

A vegetarian diet is more nuanced but try’s to avoid animal derived foods.

A Vegetarian diet is usually understood to permit eggs, fish and sometimes dairy products, but never poultry meats.  

Explore these sites for more info and recipes:

https://www.vegetariantimes.com/uncategorized/vegetarianism-in-america

https://dailyburn.com/life/health/veggan-eggs-vegan-diet/

http://dailyburn.com/life/recipes/healthy-dinner-recipes-meatless-monday/

https://www.google.com/amp/s/www.washingtonpost.com/news/food/wp/2018/08/03/you-might-think-there-are-more-vegetarians-than-ever-youd-be-wrong/%3foutputType=amp