Hola! This might be a small thing. I'm currently using Blender 4.2.9 LTS and I am wondering if there is a difference between the two. I can't seem to find subdvision in my modifiers. Just subdivision surface.
On a very technical note, if you want just subdivision then use a subdivision surface modifier and click the simple button. The surface part is the smoothing.
And now for some old man rambling: In the ancient times of the 1990's You would have to use 2 different modifiers. A Subdivision modifier and a smoothing modifier. This was when you would do box modeling, because you only had triangles. Actually quads modeling was still pretty new and only a few software packages had it.
Hola!
Yeah, there is a destructive subdivision you can do in Edit Mode. This is where you can Subdivide the mesh into editable verts, edges.
The subdivided Surface modifier adds more geometry but in a non-destructive way, where you cannot edit the extra geometry added and it makes the model file not as big as a destructive subdivided model would. Also a Subdivide Surface modifier will adjust to changes to the model easier than a non-destructive Subdivide, where you'd have to modify the mesh a lot more which could be a major chore if you have a dense mesh.
Here is a pic of the destructive subdivide cube with the Subdivide menu on the lower left and the left click menu while in Edit mode.
You probably already know this already, I'm kinda late in adding anything. just thought I'd add the Subdivide option in edit mode in case that was what you were referring to as Subdivision.
Cheers!