Ok, there's a LOT to say about overdrive pedals. Where to start, where to start.... Well I'm going to quote a member of my favorite worship band, Hillsong (the first of may to come trust me,) he says that a good reliable overdrive pedal "is like a favorite pair of jeans." That's the genius of Nigel Hendroff for you. He is. of course, correct. Having a good overdrive pedal is one of the single most important parts of having good tone, and in the end, being a successful guitar player, especially for worship.
First of all, OD versus distortion. And overdrive will almost always sound more organic, alive, smoother, warmer, and less manufactured than distortion. When you use distortion, you're going to get a very gritty and robotic sound with a lot of edge and bite. The same CAN be said for OD, but typically it's going to sound less so. To truly understand the difference, you'll have to hear it yourself.
A good overdrive can be used for many different things. Simply boosting the tone of your clean sounds is one of the first. It can ive you moreof the mids, treble or bass you want, while adding maybe a little drive when needed. It can also add drive like I just mentioned, giving you a good semi dirty tone for less intense or upbeat passages. I find the best tone for laid back songs or slow worship is a semi dirty with a lots of delay. It can also push your tone into full-on overdriven madness, which i okay too. For pure overdrive tones rather than distortion I find you get more of the guitar and amps natural tone and less coloring from the pedal or effect.
Once again, any questions so I'll know what to address next time, I am relatively new at this