Sync App Store and iTunes Store?!

I have been browsing the web for a while for an issue I fail to understand - is there any way to sync App Store with iTunes store?

Example: I purchased the app "Pocket yoga" via App Store to use on my iMac. Would I have to purchase it again in iTunes store to use on my new iPhone 4?

That was just the case with the app "Evernote": I already had it installed on my iMac, yet had to pay again for it to install on my iPhone 4.

Is there any solution to this? To include the already purchased apps on my iMac to my iPhone 4?

Cheers

Apps purchased through the Mac App Store on your iMac are for use on Macs. Not for use on iOS devices (iPod Touch, iPad, iPhone). Pocket Yoga for iMac will not install or run on your iPhone. You must repurchase it on your iPhone through the App Store or through iTunes on your Mac and then sync with your iPhone.

Also, Evernote is free.

Thanks for your reply, got it. Anyhow I ended up paying 0,99 USD for Evernote on my iPhone, hum..