Hi Guest!
Hey - did you know if you click on the title of a thread it will take you to the first unread post since you last visited that thread?
but were afraid to ask: 
STOP!! Never post your email address in open forums. Bots can "harvest" your email! If you must share your email use a Private Message or use the 
smilie in place of the real @
Pretty Please - add it to our Events forum(s) and add to the calendar! >> 
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That's a good question. The difference is subtile and I'll admit a bit confusing. I didn't really understand the difference myself when I first installed the Groups Add-On. Just think of "Group Discussions" as similar to a "Conversation"(aka Private Message). When someone creates a group (like I created this Photography group) they are given the option whether to create a forum for the group and also whether to create a group discussion area (you can set up a group with one or the other, or both, or neither).
Then, when you are setting up your group, if you check the box to create a forum and/or discussion area you are also given the option whether to make forum discussions ( or group conversations) visible to non-members. For this group, the forum discussions are visible to anyone - even non-group members but I set the group discussion area to only be visible to members of the group. I set this group to have both just to see what they looked like and what the difference was (not much practically speaking).
You could have a forum for normal group discussions that everyone, even non-members can read, then set up a group conversation section and have it for discussing group business that you don't necessarily want non-members to see.
I'm probably going to go ahead and disable the Group Discussion area for this group because there really isn't that much difference and it does tend to be confusing. One other slight difference is not obvious except to the site admin and that is that you can have different sets of user permissions for a forum versus a conversation area. Clear as mud, right?
UPDATE - Well, it looks like I can't remove the discussion area. Once the group is created, if there is a "discussion area" you're stuck with it.
Then, when you are setting up your group, if you check the box to create a forum and/or discussion area you are also given the option whether to make forum discussions ( or group conversations) visible to non-members. For this group, the forum discussions are visible to anyone - even non-group members but I set the group discussion area to only be visible to members of the group. I set this group to have both just to see what they looked like and what the difference was (not much practically speaking).
You could have a forum for normal group discussions that everyone, even non-members can read, then set up a group conversation section and have it for discussing group business that you don't necessarily want non-members to see.
I'm probably going to go ahead and disable the Group Discussion area for this group because there really isn't that much difference and it does tend to be confusing. One other slight difference is not obvious except to the site admin and that is that you can have different sets of user permissions for a forum versus a conversation area. Clear as mud, right?
UPDATE - Well, it looks like I can't remove the discussion area. Once the group is created, if there is a "discussion area" you're stuck with it.
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I don't really see a down-side to it.
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Just that it can confuse people a bit.
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Oh, that's good to know (I didn't know that - I assumed you'd only get noticed for Group forum threads you were involved in.)