I play guitar and often see people that try to use guitar effects with their basses and then share their thoughts. How do bass effects differ from guitar effects? And when does it not matter?
Sometimes it's just the color of the case, the branding (Bass Fuzz X28-B instead of just Fuzz X28), and the marketing ("As seen in Bass Magazine!").
If it goes beyond that, well obviously bass effects are designed to handle a wider range of frequencies, especially those below the normal range of a guitar.
In addition to an overall wider frequency response, bass effects may have different "sweet spots" for frequencies for some effects. For example, a wah pedal is usually factory calibrated to sweep from one center frequency (of the filter) to another. A bass wah pedal would typically be configured to sweep through frequencies about an octave lower than a guitar wah pedal.
Delay-based "modulation" effects like chorus, flanger, and phasers also usually have setting either on a knob (sometimes called "manual") or factory set which is the delay offset, and that setting controls the "center frequency" of the effect. That would normally be set lower on a bass effect.
Any digital pitch tracking effects (the Digitech Whammy pedal being an obvious example) may be configured to track certain frequencies better than others, and of course would want to be better at tracking lower frequencies or a wider frequency range when used on bass compared to guitar.
The last category I can think of is frequency mixing effects like some (analog) synth pedals or ring modulators which have internal oscillators may need to have their internal oscillator ranges tuned to work better with bass versus guitar.
In case this isn't obvious, designing effects for bass guitar can be more demanding than for regular range guitars. That's because there are important frequencies for bass that are both lower and higher than the most important electric guitar frequencies, which is actually a fairly narrow range. Also, basses tend to be played over a wider dynamic range than electric guitars. The only simplifying factor of basses is that usually bass playing is single-note, without chords. Trying to play chords through some bass-intended distortion or synth pedals can sometimes result in a messy hash, while single notes sound thick and rich.
The needs of bass guitar are closer to the needs of keyboard instruments like electric pianos and synthesizers, so any effects designed for one usually work well with the other.
For a discerning ear, the difference between bass and guitar effects almost always matters. That said, I can think of a few situations where there is not much of a market for separate effects. Certain kinds of fuzz work just as well on bass and guitar. I'm thinking about the E-H Big Muff Pi or the Zevex Wooly Mammoth. The usually give the guitar a rich low end and of course that works on bass also.
Delay pedals that have a decent frequency response usually work just as well on one or the other. Clean delay sounds need to be very neutral, so ideally you could put anything through a good delay pedal.
Some compressor pedals are full-range and work just as well on bass and guitar, but this is one area where the cheaper guitar-centered options can really kill the tone of a bass.
And sometimes a bass player might want a pedal to take away some of the dynamic range or frequency response of their bass for a certain effect.
Adding to Todd's answer - the bass chorus in particular.My Boss (others are available - but not necessarily with this feature!) has a 'low filter' facility. This specifically applies the chorus effect to just the upper frequencies if required, which cuts out the muddiness produced when low frequency notes have a chorus effect used on them. Subtle, but effective.