Of course you could copy the track and add distortion to the copy and now you have a distorted copy. Personally I would not use the words "crisp" and "clear" to describe vocals that have any distortion on them.
As with most things, the best way to get a great vocal mix is to start with a great vocal recording. When pro tracks have clarity and transparency and high quality sound for a part, that's usually because of the recording engineer and the recording quality, not because of the mix.
The most popular way to mix vocals (and therefore what you're probably hearing) is to EQ the vocals to flatter them, use one or two stages of light compression, and then automate the volume levels to keep the vocals in the right place in the mix. Some non-pros might try finding a compression that prevents the need to automate, but there really is no substitute for fader automation on vocals.
Oh yeah, don't be afraid to aggressively high-pass vocals. Depending on the mix you might even get away with a high pass at 300 Hz. Just listen for the body of the voice and make sure you don't cut that out.
Depending on the song, some vocals may be hyper-compressed to get that very up-front sound. Even with that, automation is often still necessary to keep the vocals sitting right.
Even on tracks where I'm using a single reverb for all the instruments, I find giving the lead vocals their own reverb send helps keep the vocals on top of the mix. Pre-delay greater than 50 ms usually helps keep the vocals from being stuck in the back of the room by reverb, as well as making sure you don't wet them down too much. After that it depends on the track in terms of the right kind and amount of reverb.
As I mentioned at the top, none of that is likely to clarify a muddy recording. If the original recording isn't popping, it's going to be very hard to make it something it's not.
If you want to know how to record clear vocals, then having a very quiet room and getting the right mic position are probably the two biggest ingredients. Also the singer and their voice and tone and articulation are important here. A few singers I've worked with have always sounded muffled - I never figured out why that was or if there was anything they could change about how they sang to fix that.
Regarding mic position, definitely know your polar pickup pattern and make sure the mic is being addressed properly. Pointing the mic at the nose (for a brighter sound) or at the throat (for a deeper sound) can work better than right at the mouth in some cases.
It helps to know/assess the singer and also think forward toward the whole production to get an effective vocal recording. But if there's one track in most songs that all the other tracks have to play along with, it's the vocals. By that, I mean you can take a lot of artistic license with recording vocals, especially if you record everything else so that it works well with the way you recorded the vocals.
Don't place the mic too close or too far from the singer. Using your ears and experience is the best guide here, but closer than 6" should be rare, and farther than 24" would also be a bit unusual. If you're making muffled recordings, you might have the mic too close to the singer.
I almost always have the bass roll-off (high pass) turned on at the mic and/or preamp for voice. Even supposedly "deep" voices don't need those low frequencies.