Re: "Modded Marshall"
The JVM basically is already a hot rodded Marshall. The OD channels IIRC have the most gain out of any Marshall while still doing the earlier sounds with the crunch modes. However, I still modified it. I took out C38 and switched a cap to tame the insane amounts of gain (no-one needs that much, it's too buzzy/fizzy) and fix the scratchy sound in the hi-mids. Really minor stuff. Could have probably accomplished roughly the same thing by trying different tube types but I like it now. You can just take any guitar, doesn't even need actives, could have decent passives, plug right into the front and get a great, tight, clear, punchy heavy metal distortion just like a quality high gain amp is supposed to do. I did a similarly minor mod to my Dual Rectifier (2ch) to make the red channel closer to the Revision C sound because I'm really not much of a fan of the Revision G 'grunge looseness'. I replaced the gain pot to 1M and changed the capacitor to an orange drop. Now it doesn't have the fizz problem when the gain goes past 2'o clock and all the gain it has is now actually useable. Same deal. Plug in, you get a badass sound.
I think "modded Marshall" in a general sense means "Marshall timbre with more (of something, usually gain, or whatever). You are right though. It's waaay to broad without mentioning what the modification was to what Marshall. The craze in the 80s and early 90s was to have JCM800s modded for "that Van Halen sound" which I think involved extra gain stages and so on. Dino Cazares described it as "basically like having an extra preamp in front of it and a noise gate built in." Listen to Soul Of A New Machine, Demanufacture and Obsolete. That's a Marshall. Here's a clip of playing through it.
Does it sound anything like a Marshall? Does it sound anything like Van Halen? Not really! Sure, it's bright. It's grindy, but it must have been a hell of a mod.
Kerry King goes on about some 2203 he's always used where "everything just worked". I take that to mean it's stock but he got lucky in that it already had the sound everyone else was chasing.
Then there's that modded JMP Metallica had which got stolen and naturally nobody can remember what the mods were... If you take your Marshall in to an amp tech and just ask him "can you modify this for that modded Marshall sound?" he's probably going to stare at you for a little while waiting for you to finish your sentence before asking what you're on and why you're in his place of business.
