Font manager will count all font varieties, while Writer will hide some of them. Specifically, if one font is listed as a bold or italic subtype of another font, Writer will not list the subtype. The font file will still be used when you select that particular formatting for that particular font.
E.g.: I have 20 font files for Georgia pro, but only 9 are listed in the font selector of Writer. The “semibold” and “black” (=extra bold) are listed, but “bold”, “italic” and “bold italic” ones are not there.
I guess that other software (e.g. DTP) which supports “condensed”, “light” and “black” as text properties, might provide an even shorter list. Please note, this is just a guess ; I haven’t tested it.