If so, the first # =width of casing, the second, the width of the tread.
Is wrong.
The only numbers that are meaningful are the ISO sizes, which are stated as (eg) 37-622
The first number (37) is the width, the second is the diameter of the rim that it fits. At present, the common rim sizes are 622mm (road bikes and 29er MTBs), 584 mm (newer 27.5 MTBs), and 559 mm (older 26" MTBs).
Other numbers are historical tyre sizes, and are confusing (even for Schwalbe), and best ignored. There are, for example at least 4 different 26" tyre sizes.
In the beginning tyres were sized based on rolling diameter - i.e. the outside of the inflated tyres, so a 28" tyre was 28" in diameter, and a 700 tyre was 700 mm in diameter. At the time rims were made by tyre manufacturers (Michelin, Dunlop) to suit their different tyre models, so a 28", 1 1/8" wide tyre fitted a rim that was 28 - 2x1 1/8" = 25 3/4" in diameter. and a 28", 1 3/8" wide tyre fitted a rim that was 28 - 2x1 3/8) = 25 1/4" in diameter. French sizes were in increments of 50 mm (600, 650 or 700 mm), with tyre width was indicated by a letter A (narrow), B (medium) C (wide).
As time went on, the manufacture of tyres and rims divided. The rim makers didn't want to make a huge number of different but similar rim sizes, and riders wanted different widths of tyres that fitted the rims they'd already got on their bikes. This ended up giving tyre sizes like 700x28C (a 28 mm wide tyre that fits a rim originally sized for a size C (wide), 700mm diameter tyre), or 28 x 1 5/8 x 1 1/8" (a 1 1/8" wide tyre designed to fit a rim that was originally for a 28" diameter, 1 5/8" wide tyre)
The OP's tyre is marked 700x45C and 28 x 1 5/8 x 1 3/4".
The width is 45 mm or 1 3/4"
The rim size is 700C or 28 x 1 5/8"