Different brands of the same type of EPROM often had their own proprietary high speed programming algorithms, and if they had, they were the algorithms used for programming specifically those chips. Therefore the specific algorithm for programming one brand of EPROM type 'X' will not always work for another brand of EPROM type 'X'.
However, no matter what the brand, they normally have a fallback 'slow' programming algorithm which is the same for all EPROMS of type 'X, and for those, EPROM programmers often have a 'Generic' brand category where, if you choose brand 'Generic', type 2716, you can program any 2716 using those settings, it just won't be as fast as using the specific algorithm for the brand / type might be.
Another thing to beware of is devices with different programming voltages, such as 2732 and 2732A
In general, all of these complications only apply when you are programming a device. In read mode, any 2716 or 2732, 2764 etc, can be read as if it is any brand.