it is not guitar hero at all! Here are the main reasons why it's NOT guitar hero:
1. You use your mouse clicks to click the notes or you can change it to pressing keys on your keyboard
2. It's better than guitar hero because you can edit songs, make your own beatmaps to a song you like, or adjust the song with the modifications given to you.
3. There have been big tournaments for this according to my cousin. On top of that, there an infinite number of songs to choose from and more are made every day.
4. There are 3 things in osu that you do: Hit the note, slide the note, or spin the note. You hit the regular notes, you hold the left click on the slider and follow the ball to the end and if it hits an arrow, it will go back, and the spinner has you spinning as many circles around the center as you can.
5. osu and guitar hero are spelled differently.

In short: Osu is not the same as guitar hero and osu is better than guitar hero in more ways than one.