We present 1'' resolution interferometric maps of the CO J = 2-1 and HC₃N J = 25-24 emission in the protoplanetary nebula CRL 618 obtained with the millimeter array of the Owens Valley Radio Observatory (OVRO). Our CO data trace with high accuracy the spatio-kinematic structure of different molecular components: (1) the fast, bipolar outflow, which is observed up to axial distances of ±25 (±2.7 × 10¹⁶ cm) from the nebula center with a maximal deprojected expansion velocity of V_exp ~ 340 km s^-1; (2) the roughly round outer halo, which is slowly expanding at V_exp ~ 17 km s^-1; (3) an extended structure that is elongated in the polar direction ±6'' (±8.1 × 10¹⁶ cm), surrounding the optical lobes, and that expands at V_exp ~ 22 km s^-1 (slow axial component); and (4) a dense, inner torus-like core (R_out ~ 1.6 × 10¹⁶ cm) expanding at V_exp 12 km s^-1. Components (3) and (4) have been revealed for the first time by our high angular resolution data. The geometry, kinematics, density, and temperature distribution of the individual components of the molecular envelope of CRL 618 have been constrained by fitting a spatio-kinematic model to the data. We interpret our results in terms of nebular evolution as follows. In the last 2500 yr, there have been at least two distinct episodes of mass loss at a large scale in the form of a slow wind. The first took place at a rate of 10^-5 M yr^-1 and gave place to the tenuous outer halo. The second mass-loss event started ~400 yr ago at a higher rate of ≈ 10^-4 M yr^-1, resulting in the formation of the inner dense core. More recently, the interaction between fast axial post-asymptotic giant branch (AGB) winds and the preexisting circumstellar envelope has shaped (i) the fast bipolar outflow, which is probably composed of shocked material that was originally in the inner dense core, and (ii) the slow axial component, which could represent material in the interface between the shocked and unshocked AGB envelope. Finally, we report a recent increase of the free-free continuum emission at 1.3 mm (2.1 ± 0.3 Jy) and 3 mm (2.3 ± 0.3 Jy), which could reflect changes in the activity of the fast post-AGB winds on a timescale of a few years.