An axle back replacement will only include the removal of pipes at the axle intersection, while cat again involves exchanging more of the piping system, which is typically the whole portion after the catalytic converter. Cat back installation adds more horsepower.
Cat back refers to the part of the exhaust system from the outlet of the catalytic converter to the last vent to open air. Axle back exhaust commonly attaches to the rear axle of the vehicle. The axle back exhaust system usually consists of a short radius.