The components are designed to amplify and clip the signal based off 9V supply. If you give it a different supply, the resistance/voltage/current will work differently from how it was designed. Some may still work, some won't.
For distortion pedals my guess that if you run it on a lower voltage, you won't have as much headroom, and that would also mean less clipping.
If all the technical stuff is too much to read, imagine this.
You want to go swimming. Usually they build a olympic standard size swimming pool for people to swim in. They fill 9V of water in it, and you play with whatever water there is in there.
Now you can't find a 9V swimming pool. So you making do with a kiddy pool. Can you swim in it? Yes and no. Some components don't need that much water, they can swim. Some need a lot more water or they will hit the floor. Only way to find out is to try it out.
Don't try the reverse unless you know your components can take it though. Some pedals are able to take 18V, some aren't. Make sure you know what you are doing.