Hi Georgene,
Sorry for the complexity of this answer, but I will try to explain this the best way I can. Etsy earlier this year changed the way they did categories. There are actually two DIFFERENT categories now for a listing (the old category which Zetsy supported) and the new taxonomy that Zetsy only partially supports. Below is a couple of forum topics on the subject.
https://www.etsy.com/teams/7722/discussions/discuss/15992322/https://www.etsy.com/teams/7718/questions/discuss/16748313/Perhaps the best way to explain it comes from the Etsy API descriptions:
A new-style category for Etsy listings, replacing Category. If you set the taxonomy_id property of a Listing Etsy will automatically fill in the corresponding category_id, and vice-versa. This Taxonomy can be deeper than the three levels provided by Category. We now have two taxonomies, one for sellers and one for buyers. You must use the seller taxonomy when deciding which taxonomy_id to use for a listing. The seller taxonomy is optimized for completeness and specificity. The buyer taxonomy is optimized for how buyers search on Etsy.
This is the reason for what you see in Zetsy is different than the listing which uses the new method. You can actually SEE both the old and the new.in the listing viewer. Scroll all the way to the right and you will taxonomy path and ID. he "old" categories are toward the left. Thus you can see them all in the usual output grid but with the current version you cannot change the new ones. This is a future item I intend to support - but its not there yet. I would be interested on knowing if this is a high support item or not from any other users.
Hope this long answer helps explain it. If you have additional questions let me know.