NO! Thought experiments are not merely "different from empirical, scientific experiments". For 110 years - to civilized people, this phrase has been understood to connote imaginary, i.e. unreal, fake, fictitious, phony, etc. experiments. Is a thought quasar different from an empirical quasar? Trivially - yes, empirical quasars exist in reality and thought quasars do not - because thought quasars are products of the human imagination.
If I am CAPTAIN OBVIOUS, then you are CAPTAIN OBLIVIOUS.
Is King Friday from Mr. Rogers' Neighborhood of Make-Believe different from King Amunhotep III of Egypt. Trivially, yes - because King Friday never existed as a king, who ruled over a polity in reality, but King Amunhotep III existed and reigned over Ancient Egypt for ~38 years.
Do "Things called" King Friday, Queen Sara and the Neighborhood of Make-Believe exist as a real king, as a real queen and as a real neighborhood in reality or does any reference to these make-believe (thought) things as real things fail?
If imaginary experiments exist in reality, then the imaginary King Friday, the imaginary Queen Sara and the imaginary Neighborhood of Make-Believe exist as a real king and a real queen ruling over a real neighborhood (not as sock puppets and cheap scenery in a PBS kid's show).
Mr. Rogers was a flake, but your wacky assertion that things existing in reality and things existing only in the imagination exist but are somewhat different would have sent the old boy reeling into spams of laughter, utimately culminating in his premature death.
Prefixing the word "THOUGHT" to a word which picks-out sets of human actions playing out under the objective conditions in the world (experiments) does distinguish an imaginary, THOUGHT experiment from an empirical, scientific experiment, but that is not what you are attempting to say.
Is the Easter (THOUGHT) Bunny distinct from a real bunny?
Thought experiments are imaginary experiments. They are not slightly distinct from scientific experiments. They do not occur outside of the human imagination. Likewise, the Easter (THOUGHT) Bunny is NOT somewhat distinct from a real bunny but still (in some numinous sense) exists as a real bunny. The Easter (THOUGHT) Bunny does not run around zig-zagging through fields to evade hunters, have offspring (multiply), chew on lettuce patches in suburban gardens, etc. The Easter (THOUGHT) Bunny does not exist in reality.
Is an imaginary god an existing god? You cannot be consistent in denouncing Christians for believing that their (imaginary to you) God exists - when you believe (against +110 years of this phrase's use) that imaginary experiments exist. You've committed a base-line, logical error, confounding the imaginary with the real. It - almost - makes more sense for a god to exist "in the form of thought" - than it does for an experiment to exist "in the form of thought". A god is spooky - where an experiment is not.