No, everyone has the same cap, and for the last few years the Chiefs have been spending all of it. You can carry money over from one year to the next, so some teams have more than the standard cap number available in certain years (the jags have 22 mil carrying over this year. For example).
The reason we are behind the curve at the moment is that we have basically all our stars on their big primetime contracts with the exception of Houston and Kelce. The problem is that two of the biggest contracts are for guys who are no longer worth the money. Hali and Bowe account for a nearly 20 million dollar cap hit when combined next year, and Hali had just 6 sacks, while Bowe got less than 800 yards and no TDs. Hali's contract was once justified, but, like Demarcus Ware last season, he has started to slow down and is just too expensive. Bowe has never lived up to the contract Dorsey gave him, and now that we need to pay Houston, we have to get some of that money back.
You will see this same sort of thing play out elsewhere if you pay enough attention. The Seahawks are finding success with young talent on the new rookie contracts (new as of the new CBA, so the last 5? Years), but they are starting to have to pony up. Sherman and Wilson both just got paid, and talent like golden tate and Byron Maxwell had to get let go to help accommodate that.
The Broncos have done some funny things thanks to having Manning. They knew it was all or nothing for about 4 or 5 years when they signed him. They have gone after big names in FA every season, as well as drafting skill positions high in the draft to compliment Manning. This style leads to having mercenaries on your team; veterans who have proven their ability, but are playing in their twighlight and can't land a long term, high dollar deal. They are essentially rebuilding their starting positions every season, and if you have a franchise QB and good scouts, that strategy works too. The Pats do this, as well.
Every team shuffles things around this time of year, and having a huge amount of available cap space really is a symptom of bad drafting. If you are bringing young talent in that you want to keep, you reinvest your money in that talent, and never spend huge dollars in FA, instead getting depth or place holders when necessary that way. Jacksonville is a bad team, and they don't draft well, so they let their picks walk, and end up with large amounts of space, year after year. Oakland has been bad about this, as well, but they have been drafting a bit better the last couple seasons. We have a lot of money tied up in Hali and Bowe, but we are looking to out the money into key guys like Kelce, Houston, Smith, Poe, and possibly a new WR or ILB. It's nice when you can see the solutions to problems already on the roster.