I can sizzle on an acoustic but when I try an electric guitar the sound is messy. My fat fingers are brushing the wrong strings and the pickup is picking it up. I have a tough time getting a really clear sound. Can you help me out please.
An unconventional tip might actually capitalise on your skill at acoustic.
Try turning the gain down, or even using a clean setting to practice technique.
The issue you speak of is a problem some learner electric-guitarists actually use as a crutch, letting the distortion mask mistakes - once you turn the gain down, you find they aren't fretting properly, playing wrong notes, hitting wrong strings etc.
Secondly, perhaps you can capitalise on your "fat-fingers". I have them too and use them to help mute strings I don't want to sound. For example, if playing the D-string, the tip can mute the A-string, and the lower part of your finger pad can mute the G string.
Take it slowly, and once you can fret clearly with no mistakes, raise the gain slightly. Is it still clear? Eventually, it won't be a problem but it takes time and practice.
Worth checking the fingerboard width comparisons at several fret positions. May well be that the electric is narrower, and you're just not used to it. If there is a difference, then you'll have to re-jig a lot of your fingering and patterns, or change the guitar for one of similar dimensions to the acoustic. They do exist, but it also may be the fact that the neck depth and profile is also smaller on the electric.
As ever, check where your problems actually are by stopping when it sounds duff, and noting what is going wrong, then repeating more slowly.
Try everything slowly. The string tension is lower and you're probably pushing too hard. Learn to do it slowly, with control. Speed comes naturally with control. See also another topic on this forum similar to yours
You will need to develop a lighter touch, for sure. However don't fret; it doesn't take long.