I own the DF-7 factory and was wondering if anyone knows how the overdrive acts?

Its said that if you play a tube amp a distortion pedal isnt what you want, and that overdrive is what you need instead because it doesnt change the tone. But do the overdrive settings on the pedal act just like an ordinary overdrive?

this may be hard to understand but any help is appreciated

Sunburst ESP Viper-400 with EMG combo
Ibanez Talman Elec-Acoustic
1973 Denver Acoustic
Traynor Custom Valve 20
Classic Cry-Baby