Yep, different for different credit card companies. Be sure to read offer v-e-r-y carefully. If you're going to get into this try reading a website that sspecializes in points (frugaltravelguy.com and thepointsguy.com are ones I read). Look at their Newbie guide and read postings on an on-going basis.
If you have points remaining, understand what will happen to them when you close credit card. As a general rule hotel and airline points reside with the hotel/airline and won't be affected by closing the card. TYP/UR and similar are with the credit card company and will disappear if you don't do something with them. Again make sure you understand all the ins and outs. For example, if you transfer UR points from a CSR account to a lower level account they will be worth less when redeeming. On UR cards with no annual fee (e.g., Freedom) you lose the ability to transfer the UR to your spouse or partner airlines.