These are not made-up, arbitrary definitions. Seceding is the act of withdrawing, to carry on as a separate entity. The idea of secession is a split of one organization from another. The clear implication is that the group that splits off creates their own entity, not that it simply moves over to membership into another already existing institution. That would be a transfer of membership, or a realignment.
If you don't believe me, go look up the definitions, and then how the word is actually used. I don't think you'll ever find the defection of a group from one political state to another referred to as a secession.
The states that formed the Confederacy were classsed as seceding. After the Confederacy was formed, the other states that left the Union to join the CSA also seceded. To "change allegiance" one must secede first.
For example, in the Krimml Incident the Duke seceded from Fontan to join Perdan and planned on seceding from Perdan to form his own sovereign nation.
When Westmoor (the duchy) split from Perdan (the realm) to from Westmoor (the realm), that too was a secession as they split/left Perdan. Though it was a peaceful secession, mind you.
