Web hosting provider
A web hosting provider is a company that enables businesses and individuals to make their websites available through the World Wide Web. The services that web hosting providers offer will vary but usually include website design, storage space on a host and connectivity to the Internet.
DNS hosting provider
A DNS hosting provider is a company that maintains DNS name servers, which identify your domain's location on the Internet.
If you are using the Google name servers, then Google acts as your DNS hosting provider and you automatically get 10M DNS resolutions per year. If you are using custom name servers, then the company responsible for those name servers acts as your DNS hosting provider.
For more info, learn how to manage domain name servers.