Which two moods are used for situations that are contrary to fact or for the conditions under which a situation might occur?

Situations that are contrary to fact, the mood is the conditional: third type. Example: If she had got up early, she would not have missed the bus. This example illustrates an imaginary situation; it did not happen. What truly happened was that the woman got up late and missed the bus. This was the fact. The structure is : the condition introduced by "if" carries the Past Perfect and the imaginary result carries would + perfect infinitive.

Conditions under which a situation might occur, the mood is the conditional: second type. Example: If she bought an alarm clock, she would get up on time. This statement reflects a possible solution to a problem; it is a speculative solution. She does not have an alarm clock, yet if she bought one. This is the subjunctive mood. What would the result be? She would get up on time. This is the conditional mood, second type.