So now we have, it seems, three definitions of "theism" :

(1) "Jews, Christians and Muslims traditionally share the belief that the universe was created by a personal, omniscient, omnipotent, perfectly just and good being, who has sometimes intervened in the world since then...I meant this shared conception."
(2) "Belief in the existence of a god or gods, especially belief in a personal God as creator and ruler of the world", and
(3) while ‘theism’ includes the belief in the existence of a god or gods, it is usually meant to denote belief in a personal God as Creator and ruler of the world.

It seems that (1) relies in some way on Christianity, Islam and Judaism. (2) apparently doesn't rely on them, and (3) in the end seems to be a version of (2) though with maybe more emphasis on the "personal God". (Are any gods not "personal" by the way?)  But if I understand you, you think that 2/3 is the one people "probably" understood the survey to mean? So Christianity, Islam, etc are not actually relevant; and we could also be talking about one god or several gods?

Are Christianity, Islam, and Judaism also irrelevant then to your definition of agnosticism? (I'm no longer sure what you definition of agnosticism is either.)

(Of course all this leaves aside the various definitions of theism, deism etc produced by philosophers - especially in the eighteenth century. But let's not complicate things any further...)

DA