Not quite accurate
The 33-1/3 and 16-2/3 (pretty much for voice-only applications) records were originally produced for broadcast use, and some were even in 7 inch disks. The term "long play" came about when the automatically adjusted cutting technique ("Microgroove") records were marketed. Many 45 rpm 7 inch records were produced with two songs per side using the same process. they weren't called lp, but still they doubled the playing time of standard 45's.
And the original 78s, mostly 10 or 12 inch disks, weren't vinyl, but usually hard rubber and often acetate (for so-called instant records, used in radios stations and as proofs in early recording studios). Vinyl didn't become commonplace until the early 50's or so.
