A good question, and one I am glad you asked.
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).
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.