In many, probably most, cases the three-dimensional structure of the receptor (and the ligand, if it's also a protein) is involved in the ligand interaction. A single domain of a larger protein may be sufficient, but there is a strong likelihood that the amino acid sequence of just the binding region will not form the proper structure need for ligand binding. Moreover, in many cases, the amino acid residues involved in the binding region are not continuous in the protein sequence, so it is not possible to synthesize the binding region as a short polypeptide. No doubt there are exceptions.

@Adam B Shapiro

Correction：If I isolate a motif in a domain in ligands, is it still functional? If I synthesize only the binding site region of the ligand's domain, does the amino acid sequence matter? Can Motifs or peptides function as ligands（For example, cell adhesion molecules）?

Only in rare cases where the receptor recognizes the unfolded peptide ligand, e.g recognition of tyrosine phosphorylated peptides ans proteins by by SH2 domains. The interactions between cell adhesion molecules are interactions between folded domains, frequently Ig domains. For example, see the PDB Molecule of the Month for Integrins https://pdb101.rcsb.org/motm/134 and Cadherin https://pdb101.rcsb.org/motm/99

Both Adam B Shapiro and Annemarie Honegger are right.

I would add that in my experience many peptide ligands belong to such domain families as SH2, SH3, PDZ, and WW. These short ligand sequences may be presented outside the context of the parent protein (i.e., short unstructured peptides) and can bind. A potential challenge is that much of the overall binding of family type domains to their ligands involves multiple instances. I mean the two proteins often interact via multiple motifs. Because of avidity the intact proteins may interact strongly, while individual ligand-receptor domain binding may be relatively weak and difficult to measure. Biologically this phenomenon helps provide control for signaling, providing "AND" logic.