der Abstand
distance
The spatial or physical distance between two points, people, or objects.
Bitte halten Sie einen Sicherheitsabstand von zwei Metern zum Vordermann.
Please keep a safety distance of two meters from the person in front of you.

distance
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distance
The spatial or physical distance between two points, people, or objects.
Bitte halten Sie einen Sicherheitsabstand von zwei Metern zum Vordermann.
Please keep a safety distance of two meters from the person in front of you.

The word is made up of the prefix 'ab' (separate, away) and the noun 'Stand' (standing/position). Literally, it describes the state of two things standing apart from each other or being at a distance.
Zwischen den beiden Häusern gibt es einen großen Abstand.
There is a large distance between the two houses.
To describe the distance to another object or person, the preposition 'zu' with the dative is almost always used. The phrase is 'Abstand zu etwas/jemandem' (distance to something/someone).
Der Abstand zum vorausfahrenden Auto war zu gering.
The distance to the car in front was too small.
A very common and important combination is 'Abstand halten' (to keep distance). This means maintaining a physical distance and is a central rule in many public spaces.
Im Supermarkt sollten die Kunden an der Kasse Abstand halten.
In the supermarket, customers should keep their distance at the checkout.
The expression 'mit Abstand' (by far) is used like an adverb and often appears at the beginning of a sentence or before the adjective it intensifies. It emphasizes that something is incomparably better, worse, bigger, etc.
Sie ist mit Abstand die schnellste Läuferin im Team.
She is by far the fastest runner on the team.
In a figurative sense, 'Abstand' (distance) is often combined with verbs such as 'brauchen' (to need), 'gewinnen' (to gain), or 'suchen' (to seek) to express an emotional break or distance in a relationship.
Nach dem langen Streit brauchte sie erst einmal etwas Abstand, um nachzudenken.
After the long argument, she first needed some distance to think.
clear / clearly
'deutlich' and 'mit Abstand' can both say that a difference is very large. 'deutlich' generally describes a strong extent or a clear difference. 'mit Abstand' is used especially in comparisons when something is much better, bigger, faster, or worse than all the others. So 'mit Abstand' is more focused on a ranking. If you only want to say that something has clearly become more or less, 'deutlich' fits. If something is clearly in first place or all the way at the bottom, 'mit Abstand' sounds more natural.

Dieses Geschäft ist mit Abstand das günstigste in der ganzen Straße.
This shop is by far the cheapest on the whole street.
Nach dem Training läuft Max deutlich schneller als früher.
After training, Max runs significantly faster than before.