How can a smartphone's extended battery be same size as the original battery?
Usually just marketing
Most aftermarket batteries are labelled in way that is extremely optimistic (if not an outright lie).
It is possible to change chemistries to go to one with a higher energy density, but this is usually very unsafe as the phone's internal battery charge regulation circuitry is not tuned for the new chemistry and can cause a fire or explosion as a result.
It is also possible to gain capacity by utilizing the volume better. Most cell-phone battery packs have integrated safety electronics (current-limit, thermal fuse, short-circuit protection, and/or similar safety features). Using more advanced/smaller packaging for these electronics can yield more volume for active battery material.
Similarly, you can use more advanced/thinner substrates to get more active material into the same volume -- but these improvements are typically small (maybe no more than 10% in most cases).
So...
Yeah, it's probably just a fake product built on the (probably correct) assumption that nearly all buyers will not test the battery's capacity to verify the claim (e.g. they won't get caught).