Domains are simply 'yahoo.com', or espn.com, whatever name you purchase to use is considered a domain name. Yahoo for example you can manage multiple sites on one account, and the account is simply saying they belong to you, for management and payment. Servers are just like regular computers, but have better or multiple processors, and tons of storage capacity. and yes, data is just stored in paths just like your computer, but bigger. that's why when you search for items within a database from a webpage the address bar has 100+ characters. (that and the php references as well)
happy learning.
