Physical quantities in continuously distributed matter in curved spacetime, and equations for matter and fields are considered both from the point of view of tensor theory of gravitation and on the basis of vector theory of gravitation. An example in the first case is the general theory of relativity (GTR), which uses a scalar pressure field and a scalar acceleration field. In the second case, relativistic vector fields are taken into account, including the covariant theory of gravitation, the pressure vector field and the acceleration vector field. To analyze and compare the results in each approach, formulas derived from the principle of least action and from the corresponding Lagrangian are used. The problem of correlating scalar pressure with the principle of least action in the general relativity is considered. The conclusion is drawn that results of the general relativity, when scalar pressure is taken into account, are valid for relativistic uniform systems, but in a more general case, they require correction. Three versions of general relativity were analyzed: GTR1, GTR2 and GTRm. The GTR1 version is the closest version to the standard general theory of relativity, the GTR2 version follows exactly the principle of least action, and the GTRm version is characterized by the fact that the acceleration field and pressure field are represented not as scalar fields but as vector fields. Equations for metric, equations of motion, equations for fields, formulas for the energy and momentum, which follow from the Lagrangian formalism, are presented for all versions of general relativity. An explanation is given of where dark energy comes from and what it is within general relativity.