The only time I have ever in my thirty years of life heard someone refer to a VHS as a “videotape” or “tape” is in the context of “tape that show for me”. It’s always been “Video” or if they’re specifying the format “grab the videotape” or “VHS” a lot like how people today say “DVD”.
I think we’d both agree someone who calls a “DVD” a “DVD Disc” insane and someone who just says “Disc” could mean CD-ROM, Blueray, so forth. It’s too general and I think the same thing applies to “tape”.