> first: use of dvi's w vs. right commands is not related to kerns vs. glue.
> the two are equivalent. w is simply more efficient (it reuses the given value
> instead of repeating it).

>
> second: what dvi command is used, and/or whether kerns or glue are in use at
> the tex level (interword space can't be a kern item, anyway), is not up to the
> font. the engine determines this. luatex implements dvi output differently than
> the rest. for example, take this one-line plain tex file: \nopagenumbers x y
> z.\end run through tex foo.tex && dvitype foo.dvi >/tmp/pl.typ, compare to
> luatex --output-format=dvi foo.tex && dvitype foo.dvi >/lu.typ. You'll see
> that luatex does uses dvi "right" commands where the original tex uses "w"
> commands, even with CMR. Neither is wrong.
>

Ah, you are right, it seems that DVI export from pdftex and luatex differs in
this thing. And it tex4ht recognizes `right` commands as spaces with other
fonts, so it must be issue with this particular one.

> third: it is not surprising that pdf(la)tex and lua(la)tex would find different
> fonts. i've never understood lualatex font lookup, and can't help there.
> furthermore, the actions taken by the two engines after a font is found are
> different. so little can be said there.

It is different when OpenType fonts are involved, but it should be identical
for TFM fonts. I think either Mathdesign or Hyperref must select the different
fonts with different engines. I grepped the whole Mathdesign source tree and
can't find any `lua` string, so it seems to be caused rather by Hyperref.

> fourth: neverthless, what is true is that part of the definition of a (tex)
> math font is that the interword space parameter (\fontdimen2) is set to zero.
> (that parameter is for text setting, and math spacing is totally different.)
>
> therefore, my wild guess is that whatever font is being found by lualatex as a
> result of lualatex+tex4ht interpreting
> \usepackage[bitstream-charter]{mathdesign}
>
> is, at some level, a math font. I cannot guess whether it's an issue with the
> wrong font being found by lualatex, or tex4ht wrongly considering the font a
> math font, or a bug in tex4ht's .htf file, or ... something else entirely ...

The md-chr8y doesn't seem to be math font:

md-chr8y CharterBT-Roman "TeXnANSIEncoding ReEncodeFont" <texnansi.enc <bchr8a.pfb

it doesn't have the .htf file, but the space doesn't show even when I created
one using Htfgen.

The strange issue is that different fonts are selected when compiled with pdftex and luatex. I cannot figure out how the selection works from the mathdesign source code, anyway, when I took a look at the DVI code, there is a difference:

pdftex:

set: 'what'
w: 2.678421pt
set: 'happened'
w0:
set: 'to'
w0:
set: 'the'
w0:
set: 'spaces'
w0:
set: 'between'
w0:
set: 'the'
w0:
set: 'words'

luatex:

set: 'what'
right: 2.678421pt
set: 'happened'
right: 2.678421pt
set: 'to'
right: 2.678421pt
set: 'the'
right: 2.678421pt
set: 'spaces'
right: 2.678421pt
set: 'between'
right: 2.678421pt
set: 'the'
right: 2.678421pt
set: 'words'

I am not expert on the DVI format, but I guess that font selected by luatex uses kerns instead of spaces. So maybe it is a font isssue? Can anybody confirm that?