Pilsners are lagers. The style is a pale lager that comes from Plzeň (Pilsen) in Bohemia, where Pilsner Urquell was first brewed in 1842, and the Beer Judge Certification Program (BJCP) describes the Czech original as “a refreshing pale Czech lager” brewed with Czech lager yeast and classed as bottom-fermented and lagered, according to the BJCP style guidelines.
The ale or lager label depends on the yeast and fermentation, not on color or bitterness: lagers use bottom-fermenting lager yeast and are cold-conditioned (“lagered”), while ales use top-fermenting ale yeast. German Pils, first brewed in Germany in the early 1870s as an adaptation of the Czech style, is also a lager made with clean German lager yeast, and the BJCP calls the two pilsner styles the ancestors of the most widely produced beer styles today (BJCP German Pils).
Source: BJCP 2021 Style Guidelines, 3B Czech Premium Pale Lager
Image: Würzburger Hofbräu Pilsner, photo by Christian Horvat (VisualBeo), CC BY-SA 3.0, via Wikimedia Commons.