There are two kinds of Polio vaccine in widespread use. OPV is more effective but involves an attenuated (thus, "live") polio virus in the vaccine itself, you are in effect being deliberately infected with a version of the virus that should be helpless long enough for your immune system to figure out what it is and wipe it out. Because it actually is the live virus and eventually attenuation will wear off if the virus isn't destroyed, it can "leak" working copies of the virus into a population. If everybody in that population was immunised that hardly matters, but if so why are you still vaccinating...

The injectable vaccine used in many developed countries is both less effective and more expensive, but it's "dead", so can't result in anybody getting Polio. Since developed countries do not have endemic Polio it makes sense to just bite the budgetary bullet and use a less effective and more expensive vaccine.

The killed vaccine will only be causing side effects that you'd get from injecting almost anything. Side effects like anaphylaxis - similar to if a person with a severe nut allergy ate a nut. That's a "serious but rare" one-in-a-million type problem, but in the developed world the people who administer vaccines all know about anaphylaxis and will "just" fix it like my friend with a nut allergy would if he's given food with nuts in it by mistake. It's not fun but death should be extremely rare even for that one-in-a-million if prompt intervention occurs.

A more common side effect is syncope. Especially in teenage girls, some fraction of them will faint. It doesn't really matter what's in the shot, they just do. It's often psychosomatic, so it's important other patients don't see it happen (e.g. use a curtain) or it'll spread. Alone and unsupervised syncope could be fatal (you fall down, maybe smack your head on something), but that's extremely rare when supervised, you're usually sat down to get a shot, so you should just sort of slump over and get put into recovery by the person administering the shots.

Some vaccines are associated with GBS but it's fuzzy, the numbers are all over the place - they might actually cause less GBS than not being vaccinated, given how mysterious GBS is that could even make sense, maybe getting and fighting off diseases triggers the syndrome more often than the vaccination does.