The classification agencies use for themselves belongs to an earlier era. It survives in their names and in the trade press, but in practice almost every agency does part of its neighbours' work. So use the families as a map, not as a menu.
The six families
Creative agencies invent and make the message: the idea, the campaign, the brand story, its execution.
Media agencies buy and plan the places that message appears, and measure what it returns. They earn their living differently, which makes them structurally a different kind of partner.
Digital agencies build and run: websites, apps, e-commerce, marketing automation, data. The most fragmented part of the market, because "digital" today covers a dozen genuine specialisms.
PR and communication agencies work with newsrooms, spokespeople, public opinion and internal communication. Their value sits in relationships and timing, not in production.
Activation and event agencies put something into the physical world: trade fairs, promotions, retail, events, sampling.
The specialists, the fastest growing group: one craft, very deep. Moving image, SEO, packaging, employer branding, sector agencies for pharma or B2B.
Why the labels are blurring
Creative agencies have done their own digital production for years, digital agencies do strategy, media agencies make content. Buying on the label often means buying a service the agency added to its list rather than something it is genuinely good at.
The question that does work
Not "what kind of agency are you" but "which work from my list do you do in house, with whom, and what do you outsource". The second half of that answer is the interesting one: every agency works with subcontractors, and you are entitled to know who touches your work.
IKAg's factsheets list the stated services per agency, and you can browse by expertise instead of by label.
See also: creative agency or media agency and one agency or several.