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A domain is a discrete structural unit that is assumed to fold independently of the rest of the protein and to have its own function. It can be composed of 20 or so amino acid residues to up to hundreds of them. Domains are made up of multiple secondary structure units (alpha helices, beta sheets, etc.) Most proteins are multi-domain. Folds are the core 3-D structures of domains. It is believed that only a few thousand folds exist. A beta-barrel is an example of a fold.
Motifs are short, conserved regions and frequently are the most conserved regions of domains. Motifs are critical for the domain to function - in enzymes, for example, they may contain the active sites. Another example of motifs would be muclear localization sequences.
یا به بیان دیگه
Motifs are structural characteristics and domains are functional regions (not necessarily related to size). In a protein, a particular arrangement of amino acids or secondary structure that can be found in other proteins (not necessarily evolutionarily related) can be called a motif. If that particular arrangement is related to some function (DNA or protein binding, catalytic, etc.) then it is a domain. For example, the leucine zipper motif is usually found as part of a dimerization domain in many transcription factors.