Libraries between mobile and desktop don't match

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Sortmail said:

My libraries don't match up - my mobile app has 102 resources and my desktop has 47.

This is more common than not, for at least three reasons:

1. The mobile apps have "free to use, but you do not own" resources. In your case, this is the likely reason for the discrepancy. 
2. "Personal books" created by the user on desktop are not available on mobile.
   
3. Newly released titles may not be immediately available on mobile. 

Sortmail said:

I wa going to purchase a bundle but am concerned if I buy it I won't be able to use it on both?

Nearly all resources available on desktop are available on mobile. If you have specific resource questions, please let us know. 

Does that answer your questions? 

Sortmail said:

Is there a way for me to tell what is free to use?

There isn't a list, or at least not one which is kept up to date. Is there a reason why you need to know? Your reasoning may provide insights to our user community to provide a better answer for your questions. 

Sortmail said:

I was afraid that if I purchased it through one format I would not have access to the same books in the other format.

Again, if you mean access to the resource on desktop, web, mobile, that isn't an issue. Most every resource is available across the platforms. 

Sortmail said:

I was wondering what books were free to use so I didn’t purchase those particular books  or a package that was primarily those free resources.  

The most "cost effective" way to purchase resources is through a bundle. Most bundles will likely come with some of those "free to use" resources. An advantage of purchasing them, however, is the ability to download them and use them offline.