Because the word looks sort of like "castle" (and originates from the same Latin root - castellum - via the old french chastel as castle), it would be easy to think that a château and a castle are the same thing.
The nearest English equivalent would be a "hall", "manor house" or "country house" - somewhere where a member of the ruling classes has either their power base or what we would think of as a second home in the country. This is not to be confused with the English "stately home", which is a house which has a suite of state rooms: rooms which are set aside for use by the head of state (i.e. the King or queen).
In France, this would be a château. Thorndon Hall, EssexThis is why sometimes you see Château de Versailles (in French) as Versailles Palace (in English): the French word château covers so many things. It is also why it seems that just about everyone who owns a detached home of any sort of size in the country claims it to be a château, even though it obviously isn't a castle.
The urban equivalent is a hôtel particulier , the English equivalent being the original "town house" (a word which has since broadened its scope). Buckingham House was an example of this.
A hôtel particulier, in this case the Hôtel de Sens in Paris.