Of course not. I’m not sure where you got that idea–the point of a cap and trade system is that there’s a cap. And further, the cap is set by the government, hopefully a way that decreases over time until it reaches the sustainable level (which is not zero, but is certainly much smaller than the current amount).
The only real difference between cap-and-trade vs. carbon tax is the way the carbon is priced–and a tax is a shitty way to set a price. It has to be figured out by some bureaucracy, and if they accidentally set the price too low then you end up blowing out your emissions target, and if it’s too high then you cause massive economic disruption. The “correct” tax is also a moving target, since technology improves over time and reduces the value of the emissions. Oh, and the bureaucracy has to somehow immunize themselves against massive industry lobbying.
Markets don’t solve everything, but one thing they’re almost perfect at is commodity pricing. And CO2 emissions are a commodity that needs to be priced. Cap-and-trade allows setting a hard emissions target while letting industries figure out the correct price for the emissions. It would be paid for by consumers one way or another–everything is, after all–but efficient industries would beat inefficient ones, and this allows the government to reduce the cap over time while minimizing disruption.