Cuban Lodging 101:
All hotels are government owned and belong to one of five chains: Cubanacán, Gaviota, Gran Caribe, Habaguanex, or Islazul. There's no real rhyme nor reason why one hotel belongs to one chain and not the other. It's all the state. There are some great state hotels and there are some dreary ones, along with everything in between.
Cuba has entered into joint ventures with a few foreign (non-U.S., of course) chains to manage some of these properties. The foreign-managed hotels tend to be more polished and have better service. They are still owned by the Cuban government, but bear the name of the foreign chain.
The Spanish chain Meliá is the largest of these with 28 properties in Cuba, operating under the names Meliá, Sol, Tryp, and Paradisus. They have 10 properties in Varadero.
Then there are the casas particulares (private homes). Since 1996, Cubans have been allowed to open their homes to a maximum of 5-6 guests. In the past, you had to go hunting for these, or they sent jinteros (hustlers) to entice you into their places as you walked down the street. Airbnb has just gotten into the game as the middleman for a few of the casas, and if you've arranged through them, you'll be staying in one of these in Havana.