To clarify this excellent comment: Corporations can donate to political campaigns and the organizations running them. What they can't do is donate directly to candidates running for office.
Corporations cannot donate to campaigns either. What they can do is donate to Super PACs that make independent expenditures to support particular candidates.
Campaigns for office are a subset of all political campaigns.
Post-Citizens United, corporations can engage in or financially support any political campaigning they like in whatever form, as long as they don't make financial or in-kind contributions to the electoral campaigns of individual candidates. They don't need to form a PAC to do so.