Quite some time ago, I differentiated between a server and a database by describing a server the staff at a restaurant, and the database as the storage facilities that the restaurant uses to preserve the food items.
Today we're going to differentiate between a web host and a web server (I keep adding the "web" prefix because I'm going to be using the web as a reference), a web host is a type of host and a web server is a type of server. But I'm sure that's not the differentiation you're interested in.
A webserver just like the name connotes is what helps website owners to distribute their website in a way that you can access the website with whichever device and/or browser you use. When you access a website, you don't see all the code that was written in order to build the website, you see the interpretation of the code because the server talked to your browser, shook hands on what the code means then showed you the interpretation of the code.
A web host on the other hand is a company that gathers a lot of servers, and when you pay them, they give you a server that they own, which you can use to deliver your code to the client's device. If we follow the restaurant analogy, a web host is like a franchise restaurant (like McDonald's) and a server is a restaurant (recall that a restaurant isn't just a building or a location, all the personnel in the restaurant, doing their bit to provide you with the meal is what makes a restaurant).