Yes to both questions, Jackie. I had the saloon version (sedan version, to you USns) of the same model - also very rare.
MG stands for Morris Garages, which was the name of a car dealer selling Morris motor cars in the 1920s and '30s. Their head Salesperson, Cecil Kimber, produced an alternative body for the old Morris Cowley (another fine motor!) and labelled it witht the initials of the firm. It sold well, so the exercise was repeated with many of the Morris cars over the years. Occasionally, MG have brought out a model that wasn't "badge engineered" (i.e., a standard chassis with a sexier body - and probably a higher tuned engine) - notably the MGA of the 1960s (although that shared many mechanical parts with other BMC cars.

The MG-Y series was based on the 1937(?) Morris Ten chassis, but with a totally new body and trim. Its engine (the XPAG,) which was a fine piece of engineering, derived from a design by Wolsley Cars, which had become part of the same firm in the late '30s.

The current offering of MG (now owned by Rover Cars) is the MGF, which is alos an individual design, but using a tuned version of one of the Rover engines. They have also just brought out some MG-badged, tuned versions of one of the Rover Saloons, in the original traditions of Cecil Kimber.

(To those who find this boring, blame Jackie for putting the nickel in my slot!)