They are both correct. If you care about encapsulation and SRP, go with the second one.
public void LogWarning() { Log(Severity.Warning); }
public void LogError() { Log(Severity.Error); }
private void Log(Severity severity) { ... };
The first one is also correct, however enums can grow and you will find yourself in a situation where you call a different methods based on the option. If you have only a few options and executer a few lines of code for them, the first one is more concise.
Also depends on how clear your API do you want. One method taking a parameter is clearly more concise then 10 methods with similar names without a parameter.