The term "contrast filter" means two completely different things
for the picture taking end and the printing end.

The colour filters for black and white picture taking
are often grouped as "correction filters" and  
"contrast filters".  Correction filters such as the
yellow Wratten 8 (K2) and the green Wratten 11 (X1)
are used to correct the response of film to make it
more like what the human eye sees. These filters have
only a fairly subtle effect with modern panchromatic
films which are reasonably correct even without a
filter.

Contrast filters are used to falsify the relative
brightness of different colours so that different
coloured objects of similar brightness will stand
out from each other instead of showing up as the same
shade of grey. Typical filters used as contrast
filters are the deep orangey yellow 15 (G), The
tricolour red 25 (A), the tricolour green 58 (B)
and the tricolour blue 47 (C5). These filters  
usually have an obvious and dramatic effect.

For instance, if you were to take a picture of
oranges and green apples without a filter, you
might discover that they were almost the same shade.
If you then shot the same picture with a red 25
filter (and about 2 1/2 stops more exposure
to compensate for the filter), the green apples
would be darker than the oranges. If you then
did the same shot with the green 58 filter,
the green apples would be light in shade and
the oranges darker.

Contrast filters in printing are completely
different. Multicontrast paper is made with
two or more differently sensitized emulsions
so that the printing contrast is affected
by the colour of the light from the enlarger.
With the number 5 filter, a small difference
in shade on the negative makes a big difference
in shade on the print. With the number 0 filter
a small difference in shade on the negative makes
only a very small difference in shade on the
print. Negatives are normally developed so that
they will produce a normal looking print with
the number 2 or number 3 filters.

It used to be usual for buy paper in several
different contrast grades. Multigrade paper
is a substitute for keeping several different
contrast grades of paper in your darkroom.
Many people find that variable contrast paper
is not as good as using different grades
of paper, but it is a major convenience.

Peter.

Which 'contrast' filters, please?

Contrast Filters such as the Vivitar Contrast filters are clear filters for
on-camera use. They are derived from motion picture technology, useful for
still work and especially some digital video which tends to be intolerant of
great contrast ranges. What they do is spread the light in the image,
diminishing highlights by throwing light into the shadows, while retaining
some good sharpness. (I do not know if they are still made!)

None of these work on the two-dimensional negative.

For lowering contrast at the print, use softer paper for starters.