Carbon offsets and carbon credits are both generic terms that are frequently used interchangeably but mean two fairly different things.
Carbon offsetting refers to the act of using carbon credits to make a claim for offsetting some of the greenhouse gas emissions generated by a company or individual. Carbon credits are the units used in the activity of carbon offsetting, so carbon offsets would then refer to the credits that have been used as a claim.
Typically a company with environmental targets will use carbon credits to offset some of their emissions. This is the most common use of carbon credits and enables organisations to claim they are carbon neutral.