What does laughing gas do during a dental procedure? Is it different from being put under?

Nitrous oxide. Or laughing gas is a drug that can decrease awareness and pain. It must be administered by someone trained in its use and proper monitoring should be utilized (a pulse oximeter at a minimum). When this drug is used, essentially you are being "put under".
Decreases anxiety. Nitrous oxide is used with a normal oxygen level so a patient is not put "under" it server to lessen anxiety for nervous patients. For long procedures or in higher doses it can cause vomiting or stomach upset. Local injection anesthesia is still needed when using nitrous oxidev gas.
Laughing gas. Nitrous oxide or laughing gas is used for mild anxiety and the effect can go away almost immediately once it is removed. Iv sedation (being put under) is done through injection of medication through an IV line and has a more permanent effect for hours later.