Nope, carbon tax is different to carbon offsets. A carbon tax is intended to put an immediate financial burden onto energy producers and/or consumers commensurate to the environmental impact of the power production and/or consumption.
From a corporations perspective, it makes no sense to worry about the potential economic impact of pollution which may not have an impact for decades. By adding a carbon tax, those potential impacts are realised immediately. Generally, the cost of these taxes will be passed to the consumer, affecting usage patterns as a potential direct benefit but making it a politically unattractive solution due to the immediate cost of living impact. This killed the idea in Australia, where we still argue to this day whether it should be reinstated. It also, theoretically, has a kind of anti-subsidy effect. By making it more expensive to "do the wrong thing" you should make it more financially viable to build a business around "doing the right thing".
All in theory. I don't know what studies are out there as to the efficacy of carbon tax as a strategy. In the Australian context, I think we should bring it back. But while I understand why the idea exists and the logic behind why it should work, I don't know how that plays out in practice.