Critical behavior and structural change during the phase transitions of charge-density-wave (CDW) states on In/Cu(001) and In/Si(111) have been studied by surface X-ray diffraction (SXRD). The In/Cu(001) surface exhibits critical behavior of the two-dimensional Ising model, indicating an order-disorder transition at T=345 K, ∼60 K lower than the electronic metal-insulator transition (MIT). It has been found that the scale-down of lattice correlation to the CDW correlation length (∼60 Å) causes instability of the CDW state, giving rise to MIT. For In/Si(111), the superstructure spot belonging to CDW shows an intensity drop in a temperature range (115-125 K) where MIT also takes place without critical scattering and with concomitant intensity increase of the other spot. Considering other experimental and theoretical results, we suggest a pseudo-first-order transition mechanism.