I know it means “horns”, but what horns? French horns, english horn, something else?
You can ascertain that by considering the period during which the music was originally composed.
In all periods, ‘corni’ refers to any instrument that is conical in design, rather than cylindrical. By this I mean, the borehole of the instrument itself is uniformly narrower as you approach the mouthpiece and uniformly wider as you approach the resonance bell. In a trumpet, trombone, or tuba for examples, this is not strictly the case. One notable exception would be the ‘Wagner tuba’ which is actually a true horn, specifically designed to be tapered differently and uniformly as a horn but functional in the register of a tuba. The natural horn, German horn, English horn and French horn are more common examples of ‘corni.’
If the size of the borehole differs within the instrument for various effects, this makes it not a true ‘horn’ as modelled after the animal horns originally used as ‘corni.’ Even when valves simulate changes in the length of the tubing within the instrument, true ‘corni’ maintain their conical and tapered shape throughout. Composers typically have particular instruments in mind when they use the term in musical notation, but which ones specifically were intended can only be determined by considering the musical period during which his or her options were available, or most popular and likely to be envisioned as an ideal fit for the composition.