申し込む

to apply for/to make an application/to propose (marriage) /to offer (mediation) /to make an overture (of peace) /to challenge/to lodge (objections) /to request (an interview) /to subscribe for/to book/to reserve

申込む

申し出る

to report to/to tell/to suggest/to submit/to request/to make an offer/to come forward with information