The word "forum" was chosen for the search box because you're searching not only discussion, but also users. In the future it will also search tags probably.
Regardless, as Wombat at just posted, look at the definition of the word "forum":
1 a meeting or medium where ideas and views on a particular issue can be exchanged: we hope these pages act as a forum for debate.
• an Internet site where users can post comments about a particular issue or topic and reply to other users' postings; a message board.
There's nothing inherent about how discussions are structured (flat or not) in the word.
