Understanding the relationships between the molecular nonlinear optical (NLO) properties and the bond-length alternation (BLA) or π-bond-order alternation (BOA) along the molecular backbone of linear π-conjugated systems has proven widely useful in the development of NLO organic chromophores and materials. Here, we examine model polymethines to elucidate the reliability of these relationships. While BLA is solely a measure of molecular geometric structure, BOA includes information pertaining to the electronic structure. As a result, BLA is found to be a good predictor of NLO properties only when optimized geometries are considered, whereas BOA is more broadly applicable. Proper understanding of the distinction between BLA and BOA is critical when designing computational studies of NLO properties, especially for molecules in complex environments or in nonequilibrium geometries.