Non-revenue neutral carbon tax -
Carbon-based fuels taxed at a set rate (per tonne of CO2 equivalent) either upstream (well head, mine or point of entry), midstream (electric utilities) or downstream (energy-using industries, households or vehicles)
Some or all of the revenue raised through a carbon tax are used for government programs, and the rest may be returned to households or corporations.
Revenue-neutral carbon tax - all of the revenue raised through a carbon tax are not used for government programs (except administrative costs); revenues are recycled back through tax cuts or dividends
Fee and Dividend - revenue raised through a carbon tax or fee is returned to households on a per capita basis through regular dividends
“What is a Revenue Neutral Carbon Tax” by Stuart Collins explains how this type of a carbon tax would work.