torgh'e' is the form grammatically required in this sort of "A is B" sentences where two nouns are being equated.
So there's no difference in meaning; it's just a grammar rule that you need -'e' in this situation.
A literal translation might be "As for Torg, he—not a woman."
The suffix -'e' marks a noun as the topic and can be literally translated as "as for..." The literal translation of this sentence would then be:
As-for-Torg, he-not woman.
"As for Torg, he is not a woman."
The topicalizer -'e' has to be used because you are using the pronoun ghaH ("he/she/singular they") to mean "to be."
EDIT: Hadn't seen mizinamo's reply.
Thank you! I had some experience with the KLI course before this, and have had TKD for a long time. I was also in and out of the Facebook group when I used that site, and make extensive use of Tatoeba.
I've honestly been waiting for this course for a long time. For a long time I have theoretically understood the grammar of Klingon, in an abstract sense, but it was the vocabulary and specific prefix/suffix memorization that I struggled with.