For most of the production life of the NID, they had a plain horizontally grooved butt plate. Here on a No. 5E --
435837 11.jpg
Here on a Field Grade --
Butt Plate, NID Field Grade 410-Bore.jpg
On the Lefever Nitro Specials they used the curved lines.
191014 04.jpg
Here on an A-Grade
301420 06.jpg
The butt plates with the horizontal grooves and the
Ithaca Gun Co., Inc. at the bottom were primarily used on the Model 37s, but did appear on a few of the very last post WW-II NIDs --
Late Ithaca Butt Plates.JPG
Also on a few NIDs restocked by Ithaca in the 1950s and 60s. Note that 1946 vintage, high condition, Nitro Special Brian provided a link to, 356035, has this butt plate.