For any pair of distinct non-antipodal points, a unique great circle passes through both.
For any triple of distinct non-antipodal points a unique small circle passes through all three.
Every circle has two antipodal poles (or centers) intrinsic to the sphere.
Concentric circles are sometimes called parallels, because they each have constant distance to each-other, and in particular to their concentric great circle, and are in that sense analogous to parallel lines in the plane.
If the sphere is isometrically embedded in Euclidean space, the sphere's intersection with a plane is a circle, which can be interpreted extrinsically to the sphere as a Euclidean circle: a locus of points in the plane at a constant Euclidean distance (the extrinsic radius) from a point in the plane (the extrinsic center).