Ultrahigh-resolution (ΔE = 7 meV angle-resolved (ARPES) and angle-integrated (AIPES) photoemission spectroscopy have been performed on optimally doped Bi2Sr2CaCu2O8 (Bi2212) and La1.85Sr0.15CuO4 (LSCO). The ARPES spectrum of Bi2212 at the (π, 0)-(π, π) crossing shows a pseudogap at EF above Tc, which is smoothly connected from the superconducting gap across Tc and closes slightly above Tc (T* = 110 K). On the other hand, the AIPES spectra both in Bi2212 and LSCO show a remarkable depletion of the density of states in a relatively wider energy (100-150 meV) region near EF. The temperature-induced filling of the depletion persists far above Tc and T*. This suggests that there are two different pseudogaps in the high-Tc superconductors; one is likely associated with pairing and the other is attributed to the development of antiferromagnetic correlation.