Why does initializing a string in an if statement seem different than in a switch statement?

That is because you did not specify what season has to be in the default case. What happens when month is not within 1-12? season will not be initialized.

If you are expecting strictly only 1-12 as month input, then you might want to consider throwing an Exception in default:

default:
    throw new IllegalArgumentException("Invalid month");

In your first example, there is no path through the code that fails to assign a value to 'season'. In the second example, the default case does not assign a value, so the last print ("May is...") can be executed with an uninitialized value.

In your if/else code, there is an assurance that the variable season will get a value. That is, the else statement.

Your switch code does not have it. Look what will happen to the variable season if the given value for month is 13 -- it will not get a value, and will remain un-initialised.