When should the xlsm or xlsb formats be used?

They're all similar in that they're essentially zip files containing the actual file components. You can see the contents just by replacing the extension with .zip and opening them up. The difference with xlsb seems to be that the components are not XML-based but are in a binary format: supposedly this is beneficial when working with large files.

https://blogs.msdn.microsoft.com/dmahugh/2006/08/22/new-binary-file-format-for-spreadsheets/

.xlsx loads 4 times longer than .xlsb and saves 2 times longer and has 1.5 times a bigger file. I tested this on a generated worksheet with 10'000 rows * 1'000 columns = 10'000'000 (10^7) cells of simple chained =…+1 formulas:

╭──────────────╥────────┬────────╮
│              ║ .xlsx  │ .xlsb  │
╞══════════════╬════════╪════════╡
│ loading time ║ 165s   │  43s   │
├──────────────╫────────┼────────┤
│ saving time  ║ 115s   │  61s   │
├──────────────╫────────┼────────┤
│ file size    ║  91 MB │  65 MB │
╰──────────────╨────────┴────────╯

_{(Hardware: Core2Duo 2.3 GHz, 4 GB RAM, 5.400 rpm SATA II HD; Windows 7, under somewhat heavy load from other processes.)}

Beside this, there should be no differences. More precisely,

both formats support exactly the same feature set

cites this blog post from 2006-08-29. So maybe the info that .xlsb does not support Ribbon code is newer than the upper citation, but I figure that forum source of yours is just wrong. When cracking open the binary file, it seems to condensedly mimic the OOXML file structure 1-to-1: Blog article from 2006-08-07