Why the Iowa class looks like a battlecruiser beside Montana

Does the Iowa class become a battlecruiser when compared with the Montana class?

Yes in a same-generation comparison: Montana emphasizes armour and firepower, while Iowa emphasizes speed and firepower; without Montana, Iowa becomes the battleship standard.

Classification becomes relative when a navy builds two capital-ship types in the same generation. Montana emphasizes armour and firepower at somewhat lower speed, while Iowa emphasizes speed and firepower with less protection. In that pairing, Montana fills the battleship role and Iowa the battlecruiser role even though Iowa is more heavily protected than many earlier battleships. Once Montana is cancelled, Iowa becomes the navy's battleship by default because no heavier contemporary comparison remains. An earlier exchange makes the lineage explicit: fast battleships sought battlecruiser speed while restoring more protection, so the battlecruiser concept helped generate the fast-battleship type. North Carolina and South Dakota remain battleships in this scheme because they belong to the preceding generation rather than Iowa's direct Montana comparison. The same reasoning helps explain why Hood can be read as a fast battleship when her intended battleship counterparts were not built. The Royal Navy's postwar preference for fast G3-type ships also reflected expectations of mobile task-force operations rather than another static Jutland.