The density profile rho(z) and Gibbs adsorption Gamma of a near-critical fluid confined between two identical planar walls is studied by means of Monte Carlo simulation and by density functional theory for a Lennard-Jones fluid. By reducing the strength of wall-fluid interactions relative to fluid-fluid interactions we observe a crossover from behavior characteristic of the normal surface universality class, strong critical adsorption, to behavior characteristic of a "neutral" wall. The crossover is reminiscent of that which occurs near the ordinary surface transition in Ising films subject to vanishing surface fields. For the "neutral" wall rho(z), away from the walls, is almost constant throughout the slit capillary and gives rise to a Gamma that is constant along the critical isochore. The same "neutral" wall yields a line of capillary coexistence that is almost identical to the bulk coexistence line. In the crossover regime we observe features in rho(z) similar to those found in the magnetization profile of the critical Ising film subject to weak surface fields, namely two smooth maxima, located away from the walls, which merge into a single maximum at midpoint as the strength of the wall-fluid interaction is reduced or as the distance between walls is decreased. We discuss similarities and differences between the surface critical behavior of fluids and of Ising magnets. (C) 2003 American Institute of Physics.