Now you are making it hard!
SMITHS were of course a prolific supplier of Automotive Accessories to the British Motor Industry, including Jaguar. And indeed this ‘Round Heater’ was a high volume supply item, to both the accessories after-market trade, as well as to original equipment car manufcaturers. I have a couple SMITHS Catalogues, but space allocated to Heaters is minimal, so not a lot, but as best I can tell this ROUND Style Heater came during XK period in four models based mainly on heating power, the CH.1 (1-1/4kW - recirculating type), CH.2 (2 kw - recirculating type), CH.3 (special features - recirculating type), and CH.4 (2 kw - less blower, heating-ventilator type). XK120, XK140 and early XK150 all received the CH.1. But once you have the basic Model Type, the basic unit could be customised to suit specific applications, which was mostly to do with the clip-on-cover and the warm-air distribution outlets (demisting tubes and heater flaps), plus also the detail and position of the two copper water-inlet pipes, and indeed the studs provided for mounting. This was all internal SMITHS engineering/documentation, that for reasons unknown did not warrant any identification plaque on earlier heaters, but from somewhere around introduction of XK140 did get an identification plaque.
Now the Identification Plaque gives a CODE with one example original to an early 1955 XK140 FHC being CHS620/44 ……., noting FHC heaters were different to OTS/DHC due to their different mounting location/orientation (see also 1 1/4 KW output and 12 volt)
Now another SMITHS Catalogue breaks down differently various sub-models of the CH.1, CH.2 etc main Models, and indeed lists CHS620 (in amongst other CHS3xx, 4xx, 5xx, 6xx and 7xx sub-models)
I have to assume that one aspect of the customisation of this basic 1-1/4KW main model gets us to a more specific CHS620 sub-model. Now presumably there were several more detailed customisations of the CHS620 sub-model, that for the specific early XK140 FHC application was now given a fixed/specific CHS620/44 Part Number. I am guessing, that in the earlier Mark V/XK120 days the range of sub-models and then unique part numbers for specific make/model/variant car applications was a lot simpler with no need yet to affix a plaque advising exact Part Number, but by the time XK140 was introduced a plaque with exact part number was now deemed necessary. To date all confirmed XK120 original heaters have no plaque, but all confirmed XK140 and XK150 heaters do have a plaque, and with different part numbers to suit exact application (which I wont go into here).
But over and above plaque or no plaque, and variations to top cover, pipes, and mounting studs, there are also some age related changes made to the cosmetics, including the SMITHS badge.
But from what I can see, your restored painted bluish/grey heater, does look as far as I can tell to be late XK120 original.
The military green painted heater, with plaque advising CODE FHR2403/02 is indeed a CH.7 model, sub-model FHR2403 which is I think a 2 KW output Circular Heater (not sure this is a later 1950s/1960s heater and catalogues I have are not consistent, nor indeed does the plaque still show output), but you have to guess the FHR2403/02 part number could well be some special military vehicle application given the paint colour, but surely an officers vehicle as I cant see the front-line Land Rovers getting heaters
But at end of day, I seriously doubt there is much of use/value in this FHR2403 SMITHS heater of use to an XK application , maybe the cover/flaps.