I have one topic stickied in my Music topics forum. That sticky topic does not appear in the last discussions area on the front page.
To see that sticky topic, I have to enter the music forum . When I do that, then the sticky is stuck and visible in the listings for the music forum.
So, to answer your question:
Let's say I have 3 main forums "General" , "Music" , and "Movies".
I stick a topic that I see on the main page in "last discussions" and that topic belongs to the "Music" forum.
That topic does not display a "sticky" graphic next to it on the main page in "last discussions".
I can see the topic in "last discussions" on the main page, but I cannot tell that it is sticky, and over time as more topics are made, this sticky topic vanishes off the main page in "last discussions"
When I click the "Music" link on the main page and enter the "Music" forum, It takes me to a listing of current topics related only to the music forum.
Right there at the top of listings is the sticky topic shown with a sticky graphic . It does not move off of this list unless I "unstick" it.