a solar prominence is typically a structure seen on the edge of the sun against the black background of space. it often looks like an arch. it consists of hydrogen plasma held off of the surface by magnetic fields.
a solar filament is a large dark line seen across the face of the sun. again hydrogen plasma held off the surface, but over the surface facing the observer, rather than on edge.
in a sense, they are two sides of the same coin:
the filament absorbs the intense light from directly beneath then re-radiates it in all directions, with only a small amount heading directly on a line to the observer. This is why filaments appear dark on the solar disk. On the edge, we see the weaker emission component of the filament against a dark background.
that being said, i had difficulty visualizing filaments as the same structure.
this is in part due to the fact that most images which show prominences are processed in order to lighten them compared to the surface to show more detail, so prominences always seem lighter.
...until i caught a filaprom. a filament that continues off the edge of the solar disk, clearly showing a dark line arching up over the surface:
2/16/14 newport beach, ca
DMK 51, 2.5x Powermate, Lunt 60 PT B1200
*manually guided on an altazmuth takahashi teegul mount.
took quite some time to process as software would not track well on solar image moving all over the field