OK, time for some terminology:
So called because in geometry the blades physical shape is called a trapezoid.
The blade fits in the handle and is permanently held there. Half the blade is exposed for use so the blade can be turned round for a new sharp edge.
The whole blade is replaced when both ends of the blade become blunt.
This type of blade is progressively slid out of the knife body, as the end of the blade becomes blunt, it can be snapped off, exposing the next sharp segment.
Retracting trimming knives allow the blade to be fully slid back in to the body. This makes them safer if you want to put them in your pocket or for storing them in a toolbox. Another advantage is that the blade can be partially slid out to cut at a specific depth – for instance for opening cardboard boxes without damaging the contents.
Non retracting trimming knives permanently have the blade fully out, there are two reasons; 1) it makes the knife less costly to make so they are relatively cheaper to buy and 2) It actually holds the blade more rigidly than a retracting knife so more pressure can be applied to the cut – good for cutting tough materials.
In a very popular later development, a new form of non-retracting knife has been introduced that is known as a folding utility knife. This has all the advantages of a fixed blade with the added advantage that, rather like a penknife, the blade can be folded back into the handle for safe storage and blade protection.