I've shared a lot of Rick Beato's videos on social media before, but humor me. The following video has a great explanation and demonstration of the difference that the gauge of string will make.
I'm not sure which string gauges my fellow electric guitarists use, but long ago I settled on two off-the-shelf sets that go on all of my electric guitars:
That being said, I experimented for several years trying to find the gauge that I was most satisfied with when playing electric guitar. In the late 70s, I was fortunate enough to have a guitar store nearby that sold individual guitar strings. (The long lost "Sunshine Music.") So I experimented with buying specific strings and finding what worked best for me. I eventually settled on a custom set that ranged from .008 to .038, which - of course - sounds like the range for a stock .008 set, except that I had altered a few of of the the middle strings for specific tone/strength differences. Once that store folded, I was forced to go back to off-the-shelf sets.
Back in the day, I loved the Ernie Ball .008 to .038 gauge; they were bright and easy to abuse with multi-note bends. But they had one glaring problem for me: in the early 1980s I used the whammy bar - a LOT. (Hey, it was the 80s.) But with that in mind, I completely destroyed all of the strings in a gauge that light; those strings simply could not stand up to the whammy bar abuse. I eventually switched to .009 gauge just to reduce the frequency of broken strings. But the main weakness that I was running into was where the string wrapped around the ball end; that was the primary culprit for most of my string breaks. At one point in my life I would break at least one string per gig, and since I never kept the spring cover on the back of my Strats, the ball end would shoot off like, well - a bullet, which should not be confused with the Fender strings I would later use.
And that makes a great segue, because I soon discovered the Fender Super Bullet Light .009-.042 strings, which had a molded end instead of a ball end. That design change meant that I could abuse the heck out of those strings with a whammy bar and they could stand up to everything I threw at them. Since I was predominantly playing Strats and Kramers that both could use Super Bullets, they became my string of choice until sometime in the early 2000s.
All things change over time, and I eventually drifted away from my Strats and Kramers, which was primarily due to my wanting to shift back to the sound of double-coil humbucker pickups. (And yes, I could have mounted humbuckers on my Strats, but I decided to change back to Les Paul guitars... 'cause - you know - they're Les Pauls. Oh, and an Explorer, too.) However, the Super Bullet strings did not fit into the Gibson stop tailpieces, so I needed to find a new set of strings. After trying several sets, I decided on the D'Addario EXL120BT .009-.040 strings, because I wanted the strength of the .009-.015 high end strings with the lighter .022-.040 low end strings.
So, there you have it - 40+ years of electric guitar string choices condensed into a few paragraphs.