https://www.zazzle.com/custom/gift+tags?q=gift%20tags
Depending on your design and which blank you start with - when you post for sale there will be options, (eg whether it's a for a wedding or is it for a gift or a favor?)
Choose which is most suitable for you
So it will come up under one of those departments. There isn't just one that covers all of them. But it's it a straight forward gift tag - Crafts & Party Supplies > Gift Wrapping Supplies > Gift Tags & Gift Enclosures
https://www.zazzle.com/custom/gift+tags?q=gift%20tags
Depending on your design and which blank you start with - when you post for sale there will be options, (eg whether it's a for a wedding or is it for a gift or a favor?)
Choose which is most suitable for you
So it will come up under one of those departments. There isn't just one that covers all of them. But it's it a straight forward gift tag - Crafts & Party Supplies > Gift Wrapping Supplies > Gift Tags & Gift Enclosures
Their are no "proper tags" for a specific product type as tags should generally relate to the design.
I looked at the "gift tag" that is your most recently published design.
The blank you used for it is actually that for an ID badge which natively falls under
Office & School --> Office & School Supplies --> Name Tags & Badges --> Badges
But you titled yours as ...'gift tag' which becomes ... 'Gift Tag Badge' after Zazzle automatically appends the product type to it. Then you manually chose the category of
Weddings -> Décor & Party Supplies --> Packaging --> Favor Tags
and used the tags
gift tags, template gift tags, simple gift tags, happy weddings, elegant weddings
This all is massively going to confuse search results. While it's OK to come up with a creative alternate use for a product type and change the meta data to match, when there is already an existing product type and category/department (as Sarah has shown) for it, it's best just to use that.
(Also, your image templates are not working as you probably intended. If I use Replace to upload my own image instead of your default flowers on the right, I get one very large image in the center that is cut off and all I can do with it is move it up or down vertically, I can't scale it down to fit or move it horizontally.)
