The difference between Come across and Happen on

When used as verbs, come across means to give an appearance or impression, whereas happen on means to find by chance,.

check bellow for the other definitions of Come across and Happen on

Come across as a verb (idiomatic):

To give an appearance or impression; to project a certain image.

Examples:

"A business suit and briefcase help her to come across as the competent professional she is."
Come across as a verb:

To find, usually by accident.

Examples:

"In the meadow he will come across a rare flower."
Come across as a verb:

To change sides (literally or figuratively); to ask someone to work for the opposition.

Examples:

"You argued well in court but your firm doesn't pay its lawyers well, so why don't you come across to ours?"