The Center of a group of vertices is the three dimensional midpoint of an imaginary rectangular box which encloses the vertices, assuming that the box is aligned with the coordinate axes.
The Centroid of a group of vertices is the center of gravity or the average of the individual positions of the vertices.
Note the positions of the Center and Centroid of the cone below.
The cone's Centroid is very close to the base center since all vertices but the tip vertex are at the base. The cone's Center is at the midpoint of a rectangular box which encompasses the cone.