Hi, Danielle. Let's see, your 12 foot tree fit the stand but the 13 footer did not. Seems like the simple answer is to cut a foot off the tree. Actually, that is pretty close to the right answer. First, you want to be sure that you cut a couple of inches off the bottom of the tree. The tree gets water up through the trunk. When you cut the tree a callous forms on the bottom so it can no longer draw water up. You want to cut this off right before you put the tree in the stand then put water in the stand right away. Make sure that you don't let all the water in the stand evaporate or be drawn up so the butt end is exposed to the air. If air gets to it, the callous will form again. The water makes the tree more fire resistent and helps keep the needles on longer.
If cutting the tree back a little still will not let it fit the stand, you can cut back the around the trunk until it will but leave as much of the bark on as you possibly can. Be sure that you follow all the safety rules for trees. Keeping water on the base of the trunk is the most important single thing that you can do. Put guy wires up if you have kids or pets that stand any chance at all of tipping it over or if it is tippy on it's own. Inspect your lights before and during the time you are decorating it. Replace any that show any signs at all of questionable wiring, like frayed wires or wire that does not go totally and securely into a lamp holder.
Remember that a real tree is like bringing a major potential fire hazard into your house. Be prepared with fire extinguishers and a smoke alarm. Real trees are beautiful but there are way too many fires with them every year so be very careful. I put the base of our tree in water after I buy it and leave it outside until a couple of days before christmas. And we take it down on New Years Day.