While composing a message I've clicked on the Flag icon before sending. After sending it I cannot find it in my For Follow Up folder. The flag also looks different; it doesn't have a colored border.
What is the difference between the flags and why doesn't it show in my For Follow Up Search Folder?
The difference is the scope of the flag.
When composing, you've set the flag (with no colored border) for the message Recipient and will not show up in your own For Follow Up Search Folder.
The flags with colored borders are for personal use and can be easily set by clicking the Quick Flag column in your email list. These flagged items will show up in your own For Follow Up Search Folder but not at the recipient's.
Within Outlook 2010 and Outlook 2013, it is easier to see the difference for who you’ll set the flag when you open the “Custom Flag” dialog either from the Follow Up menu or by pressing CTRL+SHIFT+G.