The difference between Addition and Increment

When used as nouns, addition means the act of adding anything, whereas increment means the action of increasing or becoming greater.

Increment is also verb with the meaning: to increase by steps or by a step, especially by one.

check bellow for the other definitions of Addition and Increment

Addition as a noun (uncountable):

The act of adding anything.

Examples:

"The addition of five more items to the agenda will make the meeting unbearably long."
Addition as a noun:

Anything that is added.
Addition as a noun (uncountable):

The arithmetic operation of adding.
Addition as a noun (music):

A dot at the right side of a note as an indication that its sound is to be lengthened one half.
Addition as a noun (chiefly, legal):

A title annexed to a person's name to identify him or her more precisely, as in "John Doe, Esq.", "Robert Dale, Mason", "Thomas Way, of New York".
Addition as a noun (heraldry):

Something added to a coat of arms, as a mark of honour; opposed to .

Increment as a noun:

The action of increasing or becoming greater.
Increment as a noun (heraldry):

The waxing of the moon.
Increment as a noun:

The amount of increase.
Increment as a noun (rhetoric):

An amplification without strict climax, as in the following passage: "Finally, brethren, whatsoever things are true, whatsoever things are honest, whatsoever things are just, whatsoever things are pure, whatsoever things are lovely, whatsoever things are of good report, think on these things."
Increment as a noun (chess):

The amount of time added to a player's clock after each move.
Increment as a noun (grammar):

A syllable in excess of the number of the nominative singular or the second-person singular present indicative.

Increment as a verb (intransitive, transitive):

To increase by steps or by a step, especially by one.