DIOS MIOS Lite can load games located only on SD card.
DIOS MIOS can load games located only on USB.
I don't understand why you think it has another meaning.
DIOS MIOS doesn't "Load" from USB, it launch games located on USB. You can load it from anywhere (in fact, you load if from the NAND, it's located in the MIOS slot)
DIOS MIOS doesn't want you to copy the game from SD to USB, it just need the games to be on USB, that's all. if you put it in the wrong place, you need to copy them to the correct place before playing, not the contrary.
You can't have both your games on the same place, loaded by DM and DML.
Place the game depending on the device you want to use. If you have a big SD card, go for it and use DML, if you don't have an SD card big enough, go for USB.
Just know that DIOS MIOS has newer settings that DML doesn't have yet (like Widescreen patch).
Also, your problem about always loading Disc instead of the game : it's because you didn't set the correct version in the loader.
You need to specify to the loader which version of DM(L) you are using.
If you install v2.2, tell him that it's 2.1+ (in DMbooter, Wiiflow), or 2.2+ (in USBgx), or else it will ignore the settings and boot from the inserted disc.
Here the corresponding settings you need to select in the loaders to prevent loading always from disc:
Settings in DMbooter:
old = up to DML v1.1
New (DM 2.0-) = DML v1.2 to DML1.5, DM v2.0
New (DM 2.1+) = DM v2.1+
settings in USBgx :
1.2 -> 2.1 : DML 1.2 to DML 1.5, DM 2.0 to DM2.1
2.2+ : DM 2.2+