Yep, a lot of differences, though that number is growing smaller each day.
One of the big differences is how Native apps run vs. how a hybrid app runs.
In order to allow you to build a Hybrid app with web tools, such as HTML/CSS/Javascript, all Hybrid apps run in a webview on Android/IOS. The webview will be different per each platform, but the key thing is that since they are running in essentially a browser, you don't get all the same benefits of a native app which can rely more on the hardware to do animations and better performance.
If you are making a simple app, without a lot of animations, its hard to spot the difference. But if you are making a game, or an app that requires lots of animations or transitions, than you may notice performance issues if its a Hybrid app. Thats why they don't recommend building games using Hybrid development.
But again, every day things are getting better and better for Hybrid development. For transitions check out this plugin:
http://plugins.telerik.com/cordova/plugin/native-page-transitions#VersionHistory
Now, Hybrid apps can have native transitions between views. I tested this on both Android and IOS and its incredibly how smooth it runs, with very little optimization. And thats just one example of how things are getting better.