There are a few different ways to tile a sphere, and you'd have to decide which one of them suits your purpose.
One of the more natural tilings is the geodesic grid that Erik linked above, as it creates the familiar hexagon tiles.
(A few of them are pentagons, due to the geometry of the icosahedron)
As you're comparing to the tiles in civ I'd guess that this is the closest to what you're looking for.
If you want more flexibility in how your regions / tiles are shaped you could easily skip generating the dual for the subdivided sphere
and simply create your own groups of triangles to form regions, to achieve something more like the total war regions.
Aside from the above, I've also tried just projecting a tiled cube to a sphere, which is easy and gives these wonky-styled tiles.
With proper resolution on the grid this also works well for customized regions, without the same scale of jagged edges you'd get from the triangles in an icosphere.