It might be possible for the cartridges to be a smaller physical size but still clamp in and work OK. For instance, it's possible to get two different sizes of black ink cartridges for some printers. Difficult to say whether this could be the case with the cartridges you have without owning the printer.
I've done an Internet search but I can't find anything about compatible cartridges for that printer being smaller in size. If you type BJC-2000 compatible ink cartridges into a search engine, there are many sites showing pictures of them. I know this doesn't give an idea of the physical size but do the replacement cartridges look the same shape as those? So long as they look as if they could fit (maybe just narrower than the originals), they may still be the right ones to use.
The correct numbers for the cartridges look to be BCI-21C for the colour cartridge and BCI-21B for the black one. Are those the numbers on the cartridges you have? If uncertain about them, I think perhaps the best action would be to make a phone call or send an e-mail to the suppliers. Voice concerns about the smaller size and ask for reassurance that they have sent the right ones.
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