
NAD is the abbreviation used for nicotinamide adenine dinucleotide, the biologically active coenzyme form of vitamin B3 (niacinamide). NAD is the oxidized form of coenzyme B3 that acts as a hydrogen (H) acceptor, while NAD(H) (known as NADH) is the reduced form that donates hydrogen as part of the Krebs’ citric acid cycle and electron transport side chain.* NADH is a complex molecule composed of vitamin B3, ribose, a mineral compound called a phosphate group and another compound called adenine nucleotide that can be made in the liver and in other cells.
NAD and NADH can each be converted back-and-forth into the other form many times during the body’s energy production cycles.* They’re both involved in transferring electron pairs (energy “sparks”) during energy transfer reactions within the cell.* Chemical energy in the form of ATP (adenosine triphosphate) is produced in this cycle.*

NADH is an essential cofactor for hundreds of biological reactions, and is used extensively in the production of cellular energy (ATP).* NADH also plays a notable role in the synthesis of neurotransmitters in the brain.*
References
https://www.nowfoods.com/healthy-living/FAQs/nad-coenzyme-b-3-faqs