Those appear to be Logitech G512 "Carbon" gaming keyboards.
The first one is a variant of the ISO layout. Many ISO layouts have a smaller left shift key to accommodate an extra key to the right of it. For example, the ISO-UK layout (105 keys) has a \| key there.

The JIS layout seems to have the same shaped enter key as ISO but with the same sized left-shift as ANSI. However it has a lot of other differences not seen in your first keyboard.

The second one is the ANSI layout (104 keys).

I think these both were first introduced with the IBM Model M keyboard but aspects of the layouts originate with the IBM Model F keyboard with it's characteristically large enter key.

Nowadays almost all keyboards fall into the ISO or ANSI physical layouts, regardless of country specific key-mappings and key-markings.
Even smaller format keyboards like TKL, 75% 70% 65% or 60% layouts keep to ISO or ANSI layouts for the main block of keys.

Really small keyboards like 40% or Planck, whether ortholinear or staggered, don't really fall into either camp. Neither do most, but not all, ergonomic layouts.
