How are curtains and blinds different?
The question assumes you have to pick a side. You don't.
Curtains
Curtains are large fabric panels attached to a track above the window that come in a variety of configuration options. Fabric type, track type, header type, fullness, puddling... having control over these kind options allows you to create something for your home that is typically warmer and softer than what you can achieve with blinds.
Blinds
Blinds on the other hand are precise and practical. They control light with a quick adjustment, sit neatly in or above the window frame, and are easy to clean. They are typically more cost effective and more versatile when it comes to solving problems based on the specifics of your home.
When deciding which is right for you... the more useful question is... 'What problem am I trying to solve?