Syncing iPhone apps to my MacBook

I have purchased an app on my iPhone. When I download the app on my MacBook it wants me to pay again. I may be totally naive on this. The app is "German Vocabulary & Grammar". I cannot find anything on the app itself with my iPhone to let me know if I can sync.

I can see where you cannot directly sync to iPhone but the other apps I use do provide a way to download and sync. Any help would be greatly appreciated.

I did go to the app website but there was no info on how or if I could do that.