URL:
http://www.codeproject.com/KB/sharepoint/SwitchWPMode.aspx
BrowseDisplayMode : Represents the default display mode.
CatalogDisplayMode : Used for adding controls from a catalog of controls to a Web page
ConnectDisplayMode : Displays a special UI for users to manage connections between Web Part controls.
DesignDisplayMode : Used for changing the layout of Web pages containing Web Part controls.
EditDisplayMode : Displays a UI from which end users can edit and modify server controls
Ex:
WebPartManager wp = WebPartManager.GetCurrentWebPartManager(Page);
if (wp.DisplayMode == WebPartManager.BrowseDisplayMode)
Do action here
else if (wp.DisplayMode == WebPartManager.DesignDisplayMode)
Do action here
else
Do action here