No (he tried to explain patiently) - they all have -the- in them because they are different ways of looking at deity. The words should be understood: panthe-ism, panenthe-ism, polythe-ism and the-ism - only the -ism is etymologically/terminologically identical between them, as indeed it is with athe-ism - although it is true to say that athe-ism is (terminologically) opposed to all of them, but they are not defined by their (terminological) opposition to athe-ism, they are defined by their theistic or non-theistic beliefs about God. Your argument is like saying that biology and eschatology are about the same thing because they both have -ology at the end of them.
More like abiological system is referring to something not/without/opposed to biologic system. Anything with 'biological' in it will be referring to biological systems except 'abiological.' That is how the term is used in common vernacular and by plenty of philosophers and theologians regardless of its etymology history.
Similarly, anything that involves the *existence* of gods, no matter what type or how many or their active involvement with humanity or lack thereof, will be a type of theism.
To use a quote I think explains my position best:
"It really all depends on how you define "theism" and "atheism."
Does theism simply mean believing in any god? If so, deism is a subset of theism. Does it mean believing in a personal or interventionist god? If so, deism is not a subset of theism.
On the flip side, does atheism mean not believing in any god or is an atheist literally just "not a theist"? If the former, deism is not a subset of atheism. If the latter and theism is viewed as requiring an interventionist god, deism is a subset of atheism. If the former and theism is viewed as requiring an interventionist god, deism is distinct from either theism or atheism.
I think the general consensus on terms would hold that atheists don't believe in gods, theists believe in at least one god, and deists specifically believe in a non-interventionist or clockmaker god. Under this rubric, deism is a subset of theism and atheism is something else."
If you go up to your average person (and I'm willing to bet your average philosopher and theologian) and say 'I'm an atheist that believes in at least one god,' they will give you a weird look and move on.