Stuck, hidden, and ignored cards
Four different things come together here, with one thing in common: they change what comes up when you study, without deleting anything. A card gets stuck because it's hard for you, but you can hide or ignore any card for whatever reason you like, hard or not.
Stuck cards
A card becomes stuck when you miss it many times after having known it. Medkit spots them on its own and marks them with a Stuck tag in View cards, where you also get a filter to find them.
The default threshold is 8 misses, and you can change it in the study preferences. A stuck card is usually a sign that it's worth rewriting: splitting it into smaller cards or adding a hint.
A stuck card still comes up when you study. It's a tag, not a punishment. That's why the Stuck and Suspended filters in View cards don't overlap: if a stuck card was also suspended, it stops coming up and counts only as suspended.
Suspending a card
Suspending takes a card out of your studying entirely: it doesn't come up and doesn't count toward the totals, until you turn it back on by hand from View cards (the Suspended filter).
Suspending is triggered only by the algorithm, when a card gets stuck and you chose that action in the study preferences. By default Medkit only tags them, so if you never changed that preference you won't have a single suspended card, and that filter will show up empty. What is manual is turning them back on.
Hiding a card
Hiding a card takes it out of your studying and out of your list. It's your own tool, manual, different from suspending (which the algorithm triggers). You can undo it whenever you want from View cards.
You have it in two places. In View cards, from the card's menu. And mid-session, with Hide card inside the Take out of the session menu: the card leaves your studying and you move on to the next one.
Ignoring one part
Some cards have several parts: a Hidden words card with several blanks, a Rectangular zones card with several regions, and so on. Ignoring one part removes just that part and leaves the rest of the card active.
It's in the same two places as hiding: in View cards and, during the session, as Ignore this part inside Take out of the session. There too you move on to the next card once you confirm.
None of this erases your progress
That said, they all last until you undo them. If all you want is to set a card aside for later without changing anything about it, the tool is a different one: skipping it during the session. Skipping lasts as long as that session and changes nothing about the card.