The difference between Distant and Remote

When used as adjectives, distant means far off (physically, logically or mentally), whereas remote means at a distance.

Remote is also verb with the meaning: to connect to a computer from a remote location.

check bellow for the other definitions of Distant and Remote

Distant as an adjective:

Far off (physically, logically or mentally).

Examples:

"We heard a distant rumbling but didn't pay any more attention to it. She was surprised to find that her fiancé was a distant relative of hers. His distant look showed that he was not listening to me."
Distant as an adjective:

Emotionally unresponsive or unwilling to express genuine feelings.

Examples:

"Ever since our argument, she has been totally distant toward me."

Remote as an adjective:

At a distance; disconnected.

Examples:

"A remote operator may control the vehicle with a wireless handset."
Remote as an adjective:

Distant or otherwise inaccessible.

Examples:

"After his fall from the emperor's favor, the general was posted to a remote outpost."
Remote as an adjective (especially with respect to [[likelihood]]):

Slight.

Examples:

"There was only a remote possibility that we would be rescued as we were far outside of the regular shipping lanes."
Remote as an adjective:

Emotionally detached.

Examples:

"After her mother's death, my friend grew remote for a time while she dealt with her grief."

Remote as a noun:

Examples:

"I hate it when my uncle comes over to visit; he always sits in the best chair and hogs the remote."
Remote as a noun (broadcasting):

An element of broadcast programming originating away from the station's or show's control room.

Remote as a verb (computing):

To connect to a computer from a remote location.