The term giant elliptical galaxy does mean an extremely large elliptical galaxy. These represent only a very small percent of ellipticals but it is typical for a galaxy cluster to have one in the center, much brighter than any other galaxy in the cluster. The term brightest cluster galaxy (BCG) amounts to a criteria for identifying them in a way that can be carried out without much study and possibly automated, e.g., for studies of many galaxies. Giant ellipticals can be far larger than other galaxies in the their cluster, in some cases as more than 10,000 Milky-Way masses, and the term supergiant elliptical galaxy is sometimes used for the largest. Giant ellipticals are thought to be the result of repeated galaxy mergers, the galaxies of the cluster presumably having a fair likelihood of colliding with a central galaxy.
The term cD galaxy indicates a particular type of very large central galaxy: with a very large diffuse stellar halo. Often they have the shape of a giant lenticular galaxy, I presume resembling an elliptical galaxy, encircled by what amounts to a diffuse galactic disk. (However, they are often referred to as a type of giant elliptical galaxy.) The term cD is a Yerkes galaxy classification. D meaning essentially lenticular, with cD meaning an extremely large instance. Like (other) giant elliptical galaxies, they are though to result from mergers, a notion supported by observation of apparent mergers in progress.