Mike: The last time I took a fuel gauge apart was back in the 50s, and it had the two tiny coils I described. Probably the design has changed since then, so you're probably right.
Eleven: [C'mon, don't be shy. Tell us your name!] Jaeger was a division of the old Swiss watch company Jaeger LeCoultre, which traces its origins back to 1833. Makers of fine cars, like Rolls, Bentley and Aston martin wouldn't, of course, put the same common Smiths instruments in their vehicles as in our lowly mass-produced cars, so you would see only Jaeger in them.
So I understand that Smiths bought the instrument division, calling it British Jaeger. In that way they enjoyed a total monopoly of instruments (except for a few aagh! Lucas ammeters) installed as original equipment in British cars, the same way that Lucas had all the electrics. Ain't capitalism grand? [It is except when you allow monopolies].
So Smiths or British Jaeger - one and the same.