The difference between Bother and Vex

When used as nouns, bother means fuss, ado, whereas vex means a trouble.

When used as verbs, bother means to annoy, to disturb, to irritate, whereas vex means to trouble aggressively, to harass.

Bother is also interjection with the meaning: a mild expression of annoyance.

check bellow for the other definitions of Bother and Vex

Bother as a verb (transitive):

To annoy, to disturb, to irritate.

Examples:

"Would it bother you if I smoked?"
Bother as a verb (intransitive):

To feel care or anxiety; to make or take trouble; to be troublesome.

Examples:

"Why do I even bother to try?"
Bother as a verb (intransitive):

To do something which is of negligible inconvenience.

Examples:

"You didn't even bother to close the door."

Bother as a noun:

Fuss, ado.

Examples:

"There was a bit of bother at the hairdresser's when they couldn't find my appointment in the book."
Bother as a noun:

Trouble, inconvenience.

Examples:

"Yes, I can do that for you - it's no bother."

Vex as a verb (transitive, now, _, rare):

To trouble aggressively, to harass.
Vex as a verb (transitive):

To annoy, irritate.

Examples:

"Billy's professor was vexed by his continued failure to improve his [[grade]]s."
Vex as a verb (transitive):

To cause (mental) suffering to; to distress.
Vex as a verb (transitive, rare):

To twist, to weave.
Vex as a verb (intransitive, obsolete):

To be irritated; to fret.

Examples:

"rfquotek Chapman"
Vex as a verb (transitive):

To toss back and forth; to agitate; to disquiet.