I would like to know the difference between
If she should win the race, congratulate her.
and
If she wins the race, congratulate her.
I would like to know if there is a difference in the meaning or if one is more formal than the other.
Both of them refer to a possible event that could happen in the future. However, there is difference in nuance. The former indicates the speaker thinks the possibility of the event happening is low. However, the latter is neutral.
"If she should win the race" could be rephrased to:
I don't think she is likely to win the race, but if she happens to win the race...
"If it should rain tomorrow" could be rephrased to:
I don't think it will rain tomorrow (based on experience looking at the sky, according to weather forecast, etc.), but if it happens to rain tomorrow.
The former could be more formal than the latter.
The meaning is the same, and the should version is formal. The version without should is considerably more common.
should modal verb (POSSIBILITY) › formal used when referring to a possible event in the future:
If anyone should ask for me, I'll be in the manager's office.
Should you (= if you) ever need anything, please don't hesitate to contact me.