What is the difference between actual overhead and applied overhead?

Actual overhead is the costs you actually incurred during the period. That is, if your utility bill was x amount, then x amount is what it actually cost you. You collect up your actual costs as a debit to the Overhead account.

Applied overhead is based on a pre-determined rate and applied to Work in Process based on how much production you have had. You get this rate by taking the estimated annual overhead costs and dividing by an estimated annual activity base. The activity base is commonly things like direct labor hours or machine hours. Once you have that rate, you apply it based on how much of the activity base you actually had that month.

For example, if you estimate $500,000 in overhead costs and 100,000 machine hours for the year, you take 500,000/100,000 = $5 per machine hour. That's your rate. When January goes by you see how many machine hours you had, say 10,000. So you take 10,000 machine hours x the $5 rate and you get $50,000. So you apply $50,000 of overhead to the Work in Process account. (Crediting Overhead.)

Your actually costs could have been $45,000 or $52,000. It isn't going to exactly match, except by some infintesimal coincidence. :-)