If you are certified by the same shop and instructor, you *might* get the same diver number.
Recreational C-cards are processed automatically by computer and the certification is checked against your name, date of birth, and prior certification history. If they can be easily reconciled, then you will end up with the same number. If your name is Buffalo J. Wobblingstein, dob 29 Feb 1978, and you do your courses at the same place and with the same instructor, and the certification details are identical on your different certifcations, you will keep the same number - however if any of the details are different - for example, the middle initial is missed out, then you will receive a different number.
If your name is a bit more common - say John Smith (sorry to all the John Smiths out there), and your PICs are processed in different locations, you will get a different number; also because the PICs are processed by different PADI regional offices dependent on location of your course. If you did one in Thailand, one in Egypt, one in America, for sure you will have different numbers- PADI Asia-Pacific is not the same office as PADI America, for example. If you turn pro, you will receive a unique number that lasts forever.
If you wish, you can have your recreational diver numbers reconciled by contacting PADI. There's probably a charge for this, and if you want your cert cards to show the same number, you will need to get them all re-issued, for which there is a substantial charge. I don't know anybody who's every done this. Thousands of certifications are issued every week, and the diver number is largely irrelevant, except in possible cases of fraudulent card purchases (you can buy them in certain locations just like fake IDs). The only important information is that the card is identifiable as yours, with your photo on the back, and your cert-level on the front. That's all the dive shop really needs to know.
Cheers
C.