I've called them "cassettes" since, jeez...1969? That's what they were always called here, best as I can tell. Never heard "K7", though.
"Tape" can mean any damn thing, as you say.
"Records & Tapes" - LPs, 45s. 8-Tracks, 4-Tracks, cassettes, reel to reel (although that was more or less gone by the time I started shopping, still hi-end audio shops would sometimes carry a few. Superscope had a line in the very early 70s, iirc.