Avogadro6: Usually I don't check the friend list, but I recall him being shown online on both. Does it matter?
Not talking about your friends' list, but your chat contacts list - unless you have your chat set to friends only.
And yes, it does. The online status on your chat page is also triggered by Galaxy, which means that someone may be on Galaxy or just have it run in the background while they're not on the site. If they're on your friends' list, they should be receiving chat notifications even on Galaxy, but if they're not actively using it they won't get wind of them - from what I've read, new messages don't generate a pop-up or something that attracts one's attention.
Also, keep in mind, that if it's been a long time since you last sent them a message and they have received other messages since then, yours will be pushed down the queue, and with the constant jumping around of contacts and the washed out grey box used for them it's not that hard to miss it.
Another case is that chat notifications are not working properly for them (mine are hit and miss most of the time), so they may not have gotten one in the first place, and if you have fallen down the queue they may not think of checking for one.
There are quite a few cases to explain the situation before the "they don't reply to me" one.