How can you tell hay fever from allergies? How do you know when you have both?

Same thing. Hay fever is the "laymans" term for fall seasonal allergies. Rose fever is the same for spring seasonal allergies.
Same thing. Hay fever is the "generic" term used for allergic rhinitis. It was coined in england for the nasal symptoms noted during the haying season which was late may into june, which the grass pollen season. It is used to describe the upper respiratory problems in allergic patients, either seasonal or perenial.