There are two main coffee plants with dozens of varieties.

1. Coffea arabica
   75% of the world's coffee - but very susceptible to coffee blight which some say will eventually kill the plant off. Prefers to grow in mountainous regions. This is the original Ethopian cultivated coffee.
   
2. Robusta coffee
   A more bitter, stronger, higher caffeine plant but more resistant to environmental factors and disease.

For coffee drinks there are again dozens of recognised drinks:

• 38 types of coffee (infographic)
• https://www.seattlecoffeegear.com/learn/coffee-101/infographics/directory-of-drinks
• The anatomy of a Starbucks beverage (infographic)
• and there's bunches more here.