What kind of curvature?

In many papers of semi-Riemannian geometry, when they talk about curvature (constant or bounded) they don’t precice which kind of curvature they talk about. I know the definition of:

-Sectional curvature

-Gaussian curvature

-Mean curvature

-Principal curvature

-Ricci curvature

(and there is a genetral one, called the curvature in the sense of A.D. Alexandrov using comparison triangles).

But, how to know from the context, which curvature the author talk about? (i think may be with smooth metrics, it’s always sectional curvature? ).

When these curvatures coincid (are equal) ?

when we say for example "a manifold with constant curvature" is this always "sectional curvature ? thanks for discussing.