The mRNA itself would behave the same from person to person. The immune response and specific cells that get “infected” can vary.
The immune system works to produce cells that can produce antibodies that bind well to the antigen, the specific part that they bind to can be different from person to person. The immune system tries to avoid antibodies that also bind to other things, but it’s not perfect.
If the injection ends up getting into a vein, then the mRNA could infect heart cells, which then later get killed by killer T cells and can affect heart function in the short term. Or potentially, they could end up anywhere in the body before entering a cell.
But, the same applies to the actual virus, only to a higher degree.
When you have a live virus infection, the immune system has the full virus to target with antibodies, so the variance will be higher compared to people only getting a subset of the virus, and has more chances to overlap with things we don’t want our immune system targeting.
And a real viral infection generates copies of the virus to spread to other cells instead of just producing proteins that the immune system will target. It’s like getting another vaccine shot every time the period it takes to produce more virus copies passes, from the moment you get infected until your immune system manages to get the upper hand (though distributed very differently).
It makes sense to be wary of new things you’re advised to put into your body, but it’s also important to frame them correctly. It’s not just risk of vaccine going wrong vs no vaccine means no risk. It’s risk of vaccine going wrong plus risk of infection breaking through times risk of vaccinated infection going wrong vs risk of getting infected times risk of unvaccinated infection going wrong.