die Schere
scissors
A tool with two blades that are moved against each other to cut materials such as paper, fabric, or hair.
Gib mir bitte die Schere, ich muss dieses Etikett abschneiden.
Please give me the scissors; I need to cut off this label.

scissors / gap
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scissors
A tool with two blades that are moved against each other to cut materials such as paper, fabric, or hair.
Gib mir bitte die Schere, ich muss dieses Etikett abschneiden.
Please give me the scissors; I need to cut off this label.

The word 'Schere' (scissors) is the second part of many nouns that describe its purpose. This way you immediately know what the scissors are meant for, for example in 'Nagelschere' (nail scissors), 'Papierschere' (paper scissors), or 'Gartenschere' (garden shears).
Für diese feine Arbeit brauchst du eine Nagelschere, keine Papierschere.
For this delicate work, you need nail scissors, not paper scissors.
The figurative meaning of 'Schere' (gap) comes from the image of two blades moving away from each other. It describes a growing gap or an increasing difference between two things.
Die Schere zwischen den Gehältern von Männern und Frauen ist immer noch ein Problem.
The gap between men's and women's salaries is still a problem.
In the figurative meaning, 'Schere' (gap) is often used in the fixed phrase 'die Schere zwischen X und Y' (the gap between X and Y). Typical verbs with it are 'auseinandergehen' (to widen), 'sich öffnen' (to open up), or 'größer werden' (to grow larger).
Die Schere zwischen Stadt und Land geht immer weiter auseinander.
The gap between city and countryside is widening more and more.
In sports, especially in soccer, 'die Schere' (scissors move) refers to a trick in which the legs are crossed over the ball. You 'macht eine Schere' (do a scissors move) in order to beat an opponent.
Der Stürmer trickste den Verteidiger mit einer schnellen Schere aus.
The striker tricked the defender with a quick scissors move.
distance
'Abstand' and 'Schere' can both describe a difference between two sides, especially when that difference is growing. 'Abstand' is the more general word and only says that two things are not equally close or equally far apart. 'Schere' is used figuratively when two developments diverge, for example with incomes, prices, or opportunities. It sounds more figurative and often more serious. The words can be confused because a 'Schere' is a kind of growing gap. If you want to measure something neutrally, 'Abstand' fits. If you want to emphasize things drifting apart, 'Schere' is more precise.

In der Diskussion ging es um die Schere zwischen hohen und niedrigen Einkommen.
The discussion was about the gap between high and low incomes.
Der Abstand zwischen den beiden Werten ist heute kleiner als letzte Woche.
The distance between the two values is smaller today than it was last week.