I am continually getting conflicting answers when I as the question "what is the difference between a sea chest and a sea bay?" Is somebody here able to provide an answer to this question?

A "sea chest" used to be the luggage you hauled your gear in when trips were a year or more. (I still have the canvas sea bag I made with needle and palm in the '80s, short trips, 4 - 6 months, so need for a sea chest) It can also refer to a valve manifold of sea suction valves for ballast, fire, SW cooling, GS and bilge pumps.

A "sea bay" is attached to the ship's hull, usually just aft of the fwd ER bulkhead, vented to the funnel by a valved vent. The sea bays, P & S, are connected by a large diameter pipe, furnished with strainers and isolating valves at either end. SW suctions, for the various sea suction chests, cooling, ballast, fire pumps etc, are taken from this large diameter pipe joining the sea bays.

Icebreakers are a bit different because of the need to keep the seabay at 20C or more, in ice.

The sea bay is a tank that may be one or two frame spaces in the engineroom double bottom and extends the width of the ship. It is isolated from the sea and supplied by large diameter piping from sea chests.
The seachests are on the ship side with grates on the bottom for sea water.
The seachest supplies water through automatic valving, through the sea strainers, which can be isolated, to the seabay.
The seabay, sea strainer and sea chest are ventilated to deck.
A ship can have an inner and outer seachest located on both sides of the ship or just one on each side.

Remote actuated valves allow the SW returns to be directed to seachests or seabay depending on the temperature of the seabay.

The SW pumps draw from the seabay and circulated to coolers ect.

The trick in the ice is to keep the air and slush to a minimum in the seabay which is why you recirc the SW back into it.