Granular high-temperature superconductors (HTSs) are characterized by the hysteretic field dependences of magnetoresistance R(H) and critical current IC(H). These hysteretic effects are described within the concept of an effective field in the intergrain medium. The effective field is a superposition of external magnetic field H and the field induced by the magnetic moments of superconducting grains into intergrain spacings (grain boundaries). The magnetization of superconducting grains is determined by two contributions: Meissner (shielding) currents (MC) and trapped magnetic fluxes (Abrikosov vortices (AV)). To develop the concept of an effective field in the intergrain medium, the magnetotransport properties (R and IC) have been compared for two cases: (AV) the magnetization of superconducting grains is only determined by the trapped magnetic flux (zero external field) and (MC) HTS grains are in the Meissner state (the external field is weaker than the first critical field of grains). In a set of experiments, the main features of the hysteretic R(H) and M(H) dependences have been illustrated and the external conditions for implementing the AV and MC states have been established. It has been found that the effects of the Abrikosov vortices and intragrain Meissner currents on an effective field in the intergrain medium at the same magnetization values are noticeably different. This is a nontrivial fact that requires a thorough study of the impact of the anisotropy of the superconducting properties of grains on the configuration of the Meissner currents in them, as well as on the orientation of vortices both inside grains and near their surface. We suggest the explanation of observed stronger effect of the Meissner currents on the intergrain medium as compared with the effect of the Abrikosov vortices.