I did a post a some time ago about the correct classification for incomplete paraplegia which is Paraparetic ( paraparisis). Technically incomplete paraplegia or incomplete quadriplegia is an incorrect term.
So for reference, quadriparetic is the correct term for a spinal cord injury that causes weakness in all four limbs. Quite often Quadriplegia is also called tetraplegia so ''incomplete tetraplegia' will be known as Tetraparetic or Tetraparesis.
Level of function will differ from person to person, muscle weakness will vary from person to person....As with quadriplegia, it will all depend on injury level and severity.