Wish I could find one of those BrightEye 75 boxes used to play around with--they're as scarce as hen's teeth!

There are alternatives if you keep an eye. Snell&Wilcox, BM, Aja, GrassValley ...etc Also if you are willing to pay a premium some broadcast stores can find it and get it for you, I'm not sure if Ensemble Designs still making them.

Semantics. Some examples pulled from the B and H web site:
BMD - Mini-Concerter, the name says it (and it is NOT a card)
Gra-Vue - MIO Mini Analog Video & 2-Channel Audio to SDI Video Embedder Converter
Cobalt - BBG-ATOS Blue Box HD/SD Analog Component/Composite to HD/SD-SDI Converter with Audio Embedder
Ensemble Designs - BrightEye 75 HD/SD Analog-to-Digital Video Converter & Analog Audio Embedder
Ensemble Designs - BrightEye 25 Analog Video and Audio to SDI Converter - SDI, Analog Audio, TBC and Embedder, BNC and Multipin Connections
Bluefish444 Synapse ANA140 Analog to SDI Converter
Link Electronics LEI-560 Analog to SDI Converter
Kramer 7408 SDI to Analog Converter
AJA V2Digital Analog to HD/SD-SDI Mini-Converter

To list a few. All are signal pass-thru devices that take in an analog signal and spit out a digital signal, nothing retained, nothing saved in it. AFIKT their PC connections are used for setup, not ingesting video.

On the other hand devices such as the
BMD Mini-Recorder (which IS a card)
AJA U-TAP USB 3.1 Gen 1 Powered SDI Capture Device
do enable recording a SDI video stream to a file on the PC

DV/HDV over IEEE1394 (aka firewire, iLink) is an interesting case because it can be either a file transfer from media (e.g., tape) or a video stream from a source such as a live camera. There was the Sony Media Converter - Analog to DV - Sony DVMC-DA2, for use with sources that did not have native firewire output.

I think that I will stick with the manufacturer's nomenclature.

B&H still sells them. Are they worth it?

I've already told you "despite being called by the manufacturers converters". and I've already explained how analog capture works in an SDI device/card and how SDI signal is sent into PC, Whether you understand it or not that's a different story.
Some SDI analog capture devices use USB2 for settings control, some use old serial DB 25 connector, but they all output digital SDI and has to interface with an SDI2USB3 or SDI-PCIe, An SDI PCIe capture card can capture analog sources so it's a capture card and can interface with an SDI device so it acts as an interface card. this is probably what confused you.

Too rich for my blood. A few sold (used) in the past year for $350-$400, which is about all I would be willing to pay. I mainly just want to play around with it because it looks to be a nice piece of kit.

Worth is subjective and differs from one person to another, Keep in mind you would need a SDI interface, if you have a desktop a SDI PCIe card can be had for less $20, But if you have a laptop a SDI to USB 3.0 adapter is required, USB 2.0 won't work I learned that the hard way.

I bought mine few years ago for $200 used, but good capture gear is not cheap anymore, an analog TBC would cost more than that used.

You can easily find an AJA FS1 on ebay for under $1000. They have a TBC and Frame Sync.

"Composite/S-Video input and output with TBC"

https://www.aja.com/assets/support/f..._2.2.2.1r2.pdf