A quick tour of managing tools and toolboxes
You manage toolboxes in either the Catalog window in ArcMap, the ArcToolbox window, or in ArcCatalog. If you have any experience with Windows applications, such as Windows Explorer, you'll notice that basic toolbox management functions such as create, delete, copy/paste, and rename are found in familiar places and behave in familiar ways. For example, to rename a toolbox, you right-click the toolbox to open its shortcut menu and click Rename.
Toolboxes have a name, label, and alias property. The name and label properties are to support different languages, and the alias property is used in scripting to uniquely identify a tool and its toolbox.
Tools have a name and label property. The tool name is used in scripting and cannot contain spaces.
Toolboxes can be a file (.tbx) in a folder or an item in a geodatabase. A toolbox residing in a geodatabase has a different internal format than a toolbox residing in a system folder, and you cannot copy a toolbox from one format to another. Python toolboxes are geoprocessing toolboxes that are created entirely in Python. You cannot add tools to a Python toolbox as you can with custom toolboxes.
Once you create a toolbox and add tools to it, you need to be cautious about deleting or moving the toolbox. Suppose you create a toolbox ProjectB and a tool within it Calculate Required Fields. Over time, this tool becomes widely used by you (or others) in models and scripts. If you rename, delete, or move the toolbox, none of the models and scripts that use the tool will work.