応募【おうぼ】
application, subscription, entry (competition, raffle, etc.), enlistment
募集【ぼしゅう】
recruitment, invitation, selection, advertisement, taking applications, raising (funds, donations, etc.), collection, subscription, solicitation, flotation (of shares, loans, etc.)
募金【ぼきん】
fund-raising, collection of funds
公募【こうぼ】
public appeal (e.g. for contributions), public advertisement (of a post), open recruitment, public offering (of securities)
募る【つのる】
to become stronger, to grow in intensity, to grow violent, to become worse, to invite contributions, etc., to solicit help, participation, etc., to recruit (e.g. soldiers)