So is the detachable magazine something that makes a gun a lot more dangerous from the perspective of being able to get through lots of shots quickly? (and quickly refreshing the ability to get off more shots)
Pretty much. . . you buy a bunch of magazines, put the rounds in the magazine ahead of time and then you can switch magazines in 2 seconds or less.
For example my handguns have detachable magazines and I keep the magazines out of the gun (and locked up) but I can have one ready to fire in about 30 seconds. About 25 seconds of that is getting to the safe and unlocking it, the last two steps are load the magazine and rack the gun (which puts a round in to the chamber and draws the striker back)
Most pistols except for revolvers and most rifles except for maybe some bolt actions have detachable magazines.
Most shotguns however have an internal magazine which requires the rounds to be loaded individually into the gun which takes far more time. A lot of people on here like to defend the AR-15 by claiming that if someone used a shotgun it would be more deadly. This is where that argument fails. While yes the shotgun would be even more powerful and deadly against kids at close range loaded with either buckshot or a slug, once the user had fired off all the shells the reload process would give a lot of people time to escape or even possibly a chance to counter attack the shooter.
Here is a youtube video of loading an AR-15 a lot of it is explaining and a lot of the checks he does are of no meaning if you are in the middle of shooting people
Consider how little practice or effort it takes to do that and you get 30 rounds every load.
On the other hand here is someone showing you how to reload a shotgun fast.
Consider that he had to practice at this loading method (this isn't a natural movement) and it still takes longer to get 6 rounds.
Even if you ignore the effective range and make the argument that a shotgun is deadlier at close range (which it is) a ordinary shotgun still takes all that effort and time to reload 6 to 8 rounds. Which is why mass shooters don't carry shotguns, they carry AR's.