On here, it told me that the estimated postage would be $2.05. When I went to mail it at the PO, he told me it would be $2.45. (Plain manilla envelope with plastic wrap inside). I got curious, and looked on the USPS site, put in the postal codes, and the size and weight of the book. It quoted the price to be $1.90!

I'm so confused...if I would've printed postage online for $2.05, would the other person have gotten stuck with the rest of the owed postage?

The rates are different for First Class Large Envelopes and First Class Packages. Books unless really thin usually fall into the package category. I'm not sure what categories of the mail you got the different prices on but if there isn't enough postage on the item it could arrive postage due.

Maybe they charged you for the metal clasp on the envelope?

A metal clasp makes it not machinable.

https://stamps.custhelp.com/app/answers/detail/a_id/180/~/non-machinable-letter-surcharges

Oh, I didn't know that about a metal clasp!

Metal clasp?  . . . oh please, I receive them all the time.

Probably need more information to figure out your question Kashmir. First Class or Media Mail?  DC? 

At first glance, your numbers ($2.05 & $2.45) don't add up:
Media Mail up to 1 pound = $2.38
                     up to 2 pds.    = $2.77
First Class up to 1 oz.       = $1.22   (parcel)
                not over 5 oz.       = $1.90
                not over 6 oz.       = $2.07
                not over 7 oz.       = $2.24
                not over 8 oz.       = $2.41
                not over 9 oz.       = $2.58 

When you printed your wrapper did you have it showing only the weight of the book, not the wrapped book? Sometimes the weight of the packaging is more than PBS has alloted when you use something other that the plain PBS wrapper with tape.

Since your numbers don't match up to the list its hard to tell, but it looks like maybe you checked the under 5 oz online to get 1.90, the system added a bit for packaging to get it over the next ounce and estimated it at 2.07, but your packaging weight enough to push it up even higher at the post office.

It is always best to weigh the wrapped book if you will be using the online postage. The system gets its weights from outside sources so they can be wrong and if you are using alternate packaging, the system has no way of knowing how much weight you are adding (it only accounts for 0.6 ounce).

Thank you, Melanie! You helped me a bunch!