Hello there,
The distortion pedal and stomp box refer to effects that change the sound of a guitar. A distortion pedal is a device to alter your sound. It can may your tone sound more fuzzy. You can use a pedal (sometimes called a stomp box), you can use an effects rack or have effects built into the amp itself. The pedal is a box that sits on the floor and is connected between your guitar and the amp. It has a switch you can step on to turn it on/off. That is handy in that you can turn the effect on or off while you play without having to use your hands. The effects rack is a unit or set of units that are plugged in between your guitar and amp. To control those you have to walk over and change the settings. Lastly, some amps have various effects built into them. Generally you have to change the settings by hand, but some have a pedal on/off switch.
You do not need a distortion pedal to generate distortion. We used to do that all the time before pedals were common. You can generate feedback between the guitar and the amp. You do not have the control that you get from an effects device, but just the same you can generate a rather dramatic effect. That is especially true with old style tube amp (modern amps are generally solid state electronics). You can overdrive the old tube amp and that also generates sort of a distortion. That also was a very common technique. With modern solid state amps, you now use a overdrive pedal to try to create a similar sound.
EVH did not use distortion pedals or other distortion devices. He even used to dip his pickups to prevent hum and distortion. His gear set up did allow him to generate some distortion by way of the old school methods, feedback through the amp and over-driven tube amps. He essentially plays the way we did back in the early and mid 60s.
Later on he added some processors to his gear. While not technically distortion pedals, nevertheless, he used some effects in his sound. He also experimented with varying the power (voltage) going into the amp. But the major feature of his sound came from his old school playing style.
In case you would like to read more about his gear set ups here is a link.
http://mr5150.vhvault.com/evh-brown-sound.html
Later,