A diamond pendant is the ornamental piece that hangs from a chain. A diamond necklace is the full piece, chain included, and the term often refers to designs where the diamonds run along the chain itself rather than hanging from it.
In practice, the two terms are used interchangeably. A ‘diamond pendant necklace’ is a pendant on a chain, sold as a complete piece. When clients ask us for a diamond necklace, we usually clarify whether they mean a pendant style or a chain-set style, because the budget, chain length and styling considerations differ.