You may have heard of a radio remix or a radio edit.
I used to work in radio programming and VERY often we would play a radio-specific version of the song. This is because either a) radio wanted something stylistically different than the album version or b) the song would only get identified as a single after the album was long done and needed more production than it got during the album-production process.
Radio programmers are NOTORIOUSLY picky – and often quite conservative with which songs they will add. And no, it's not because “radio hates anything unique.” Ok maybe they do a liiiiiittle bit, but there's a REASON for it.
You have to remember that the worst thing for a radio station is that a listener in their demographic could change the channel. If the listener jumps to a different preset, you may not see them back for DAYS. Repeat this too many times and the listener starts to favor the other station.
This means that a song you are playing has the potential to hurt you WAY MORE than the song you AREN'T playing. Listeners rarely think “man, why aren't they playing this other song,” they're only thinking about the song they're hearing and if they like it or not. So good stations know they have to be very confident that the song will do well before they add it. My old boss would sometimes wait 6 months after the impact date just to see how it would test at other stations first.
The other concern stations have is about keeping things moving. They want it to feel energetic yet have some dynamic to the flow. That means getting to the point, then moving on. They're not going to play songs that have 32-measure instrumental sections or repeat a bridge 8 times (if you're into worship music, go look up the radio edits of the songs and you'll see how they chop down all the bridges lol).
I found a part of keeping things moving is even needing some sections beefed up compared to an album version of the song. We would regularly play songs that one of the main differences between the single and the album was that they had more percussion sooner and the song's builds would all get pushed forward a little. That's not to say radio WON'T play a soft song, but it still needs to have some oomph to it.
The other thing about making a dedicated radio version of the song is that you need all the help you can get to compete with the other songs also going for adds. Many stations only have 20-30 “current” slots. If you can make some tweaks to make it fit the format a little more, the better.
On the subject of formats, it's also important to remember that stations have to have formats to survive. They have to pick a target demographic and specific genre and stick to it in order to retain listeners. They're also in the business of building true fans and superfans.
Here's a version of a song we produced for Anthem Worship. The first version is the one you'll hear on the album, and the second is the radio remix we did. You'll here that because the song is so dynamic, we had to figure out how to give the first verse and chorus a little more oomph while still retaining the build of the song. The other thing we did was give the song an intro that announcers could talk over (or room for a station liner). It's a tough balance because you also don't want a long, drawn out intro either.