If you use a # hashtag on twitter, it marks the tweet with that topic. They are used for topics. If you make a tweet about birds, you would say #birds.
On the other hand if you want to send a tweet that's to a particular Twitter user or other person in the world, then you use an @ symbol to say the tweet is addressed to that person. I have used it on Facebook if there is a post, and a whole bunch of comments, and I want to respond to one of the comments, but it's not the most recent comment. @