For this answer lets restrict ourselves to T dependent MHC II mediated responses.
So, an APC like a macrophage or a dendritic cell, takes in a pathogen by phagocytosis and degrades it inside the cell. Some of its broken proteins, which are antigens are presented on the MHC II of this particular APC.
The B cells also do something similar but they identify either free floating antigens or the ones that are expressed by phagocytic APCs. These antigens are broken down in the lysosome. These fragments now are expressed on the surface along with MHC II. This fragment may or may not contain the epitope that the B cell receptor (surface antibody) originally recognised the antigen with. Also, it is not that just one of the fragment is taken to the surface, most of them make it, each with a separate MHC.
The T cell that is going to now interact with this B cell may have a TCR (T cell Receptor) against the epitope in any one of those fragmented antigens on the MHC.
This T-cell is specific to that particular epitope of the antigen it bound to, similarly there could be another T-cell that could recognise some other fragment of the same antigen brought to the membrane by a different MHC II.
So, the epitope that the B-cell and the T-cell recognised the antigen with, needn't be the same. But logically, there's a possibility that they may be.
- The processing of antigen in the phagocytic APC is not shown in the picture.
- B cell recognises antigens not that are displayed on the MHC II (this the T cell does) but those that are tethered on the APC membrane.
Image: Nature Reviews Immunology.