What determines which font styles appear in the drop-down list of the formatting toolbar?

I came to notice that in different operating systems different font styles appear in the drop-down list of the formatting toolbar of LibreOffice Writer (don’t know about other modules) – having the same LO version in use.

For example, in Debian 8 the font Lato appears only with its regular style in the drop-down list.
If I want to use the styles Light, Thin or others, I have to select them via “Format” > “Character” (or right-click > “Character”).
This is not only inconvenient, it also has another major downside:
When I open a document that was created (and formatted) under a different OS, and a font was originally selected via the drop-down list, a different font is chosen if the originally used font is now not available in the drop-down list – and I have to re-format all the text with that particular font.

Another example is the Light style of the font Aleo, which doesn’t appear in the list using Windows 8.1, Ubuntu 16.04 and Debian 8.
On the other hand – and strangely enough – in Ubuntu 16.04 I can now not only choose Calibri and Calibri Light from the list, but also Calibri Light Italic (!). I can normally never choose an italic style from this list. How come that now I can?
It seems a bit like LibreOffice “does what it wants” in this regard.

What determines which of the installed font styles appear in the drop-down list?

Does it have something to do with the way the fonts are installed?
Or does it depend on a certain configuration in the operating system?
Does it maybe do have something to do with the version of LO?

LibreOffice displays the fonts that are installed and available on each individual system. These include those provided by LibO, those provided by the operating system, for example Calibri by Windows, and those a user has installed themselves, for example the font Aleo which can be downloaded from the internet. Each font has a separate name which is shown in the LibO dropdown list.

Some fonts exist in several forms for example DejaVU Sans, DejaVu Sans Light, DejaVu Serif, DejaVu Serif Condensed etc. which shows as six entries on my font selection.Whereas Bold, Italic, Underline etc. are variations on each font and can be selected by Format > Text.

Calibri, Calibri Light, Calibri Light Italic are examples of the former like DejaVu, and each font will be shown in the drop down list. As they are Ms fonts, these fonts would not normally be installed on an Ubuntu system where would would use Liberation.

If you regularly use LibO on multiple systems, you need to select the same fonts on each system. In my case I use the Franklin on my systems, but revert to a more orthodox set when I send documents elsewhere. LibO has a font replacement table to be used for documents using fonts not installed on the current system.

Hi Peter!
Regarding your first paragraph: Yes, clear. But the last sentence is exactly what does not apply, which is the root of my problem (and question).
Paragraph 2: Also clear, but Aleo Light does not show up in the dropdown list!
Paragraph 3: Calibri Light Italic should not show up in the list, as you correctly stated and explained in paragraph 2. But it does.
Paragraph 4: I do use the same fonts on every system, but - as I wrote - they are being handled differently.