A tag is a label you put on one exact copy of a card: this Lightning Bolt in this binder, not every Lightning Bolt you own. Use tags for whatever you keep track of: trade fodder, signed, borrowed, to sell, cube.
Long-press a card in a binder, deck, brew, or list and pick Tags. In a deck, only copies you own can be tagged. Tick the tags you want on that copy, or type a name to make a new one. A tag shows on the card as a small chip: in a panel that peeks out under the row in list views, and down the right edge of the art in grid views.
Global tags travel with the card. Move a copy to another binder and they come along. Combine two stacks and their tags merge. Export your collection and the tags are in the file; import it back and they land on the right cards. Tags that come back through a collection import are global tags; a backup restore brings back exactly what you had, local tags included.
A global tag is offered everywhere. Make it once and it is available on every card in every binder, deck, brew, and list.
A local tag belongs to one place. When you make a tag from inside a binder, deck, brew, or list, switch on Only in this binder (or deck, brew, list) and the tag exists only there. It is offered in that place's picker and nowhere else, though a binder, deck, or list tag's chip still shows on All cards and All lists, where you can also filter by it. A card that leaves the place leaves the tag behind.
Each place can hide global tags. Open the edit screen of a binder, deck, brew, or list and find the Tags section. The Offer global tags switch turns global tags off just there: they are not shown on the cards and not offered in the picker. While the switch is off, every new tag you make in that place is local to it. Nothing is deleted, and switching it back on brings them back.
Binders, decks, brews, lists, All cards, and All lists have a Tags filter. Type to find a tag and pick it, the same way you filter by set. The list narrows to cards carrying any of the tags you chose.
Settings → Tags lists your global tags with how many cards each one sits on. From the menu on a row you can rename a tag (it changes everywhere at once), merge two tags into one, or delete one. Deleting a tag takes it off every card; the cards stay.
Local tags are managed where they live. The Tags section in a binder, deck, brew, or list edit screen lists that place's own tags with the same rename, merge, and delete menu.
Not in the same place. Two global tags cannot share a name, and a local tag cannot share a name with another local tag in the same binder, deck, brew, or list. A local tag may share a name with a global one. When you try to rename a tag to a name that is taken, the app says the name is taken and points you to Merge.
It goes with the binder. You empty a binder before deleting it, and each card loses that binder's local tags on the way out, keeping its global ones.
No. Tags wear the app's chip style so they read the same on every theme.