A protein domain is a conserved part of a given protein sequence and (tertiary) structure that can evolve, function, and exist independently of the rest of the protein chain. Each domain forms a compact three-dimensional structure and often can be independently stable and folded.
On the other hand, a motif is a distinctive sequence on a protein or DNA, having a three-dimensional structure that allows binding interactions to occur. Early on, clustering was used to detect common three-dimensional structural motifs in proteins.
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