I’m very familiar with the Object and Bone types when I parent objects. But I’m not sure about the Armature type. In fact, even if Ctrl+P, Armature Deform manipulation parent the mesh to armature, Parent Type is Object. What is the difference between Armature type and Object type?
That is the old way to deform a mesh with an armature.
It creates correspondence between vertex groups and bones or envelopes and vertices without the need of adding an armature modifier to the mesh.
The modifier is more flexible.
It allows to mix effects of envelopes and weight groups.
It has an option to preserve volume.
And it can be placed after other deformers (after a mirror modifier, for example).