Hope this helps
1: Node Selection Tool. Doesn’t have a viewport Gizmo (the technical name) and no Viewport movement or adjustment capabilities, it is just a selection tool nothing more.
2: Is the Universal Tool, which has all three Gizmos in one; Rotation, Translation and Scaling handles.
3: Rotation Tool: Rotation Gizmo only
4: Translation Tool: Translation Gizmo only
5: Scaling Tool: Scaling Gizmo only
6: Active Pose Tool: When engaged it allows you to grab a bone, like say a hand and when you move the hand the arm, shoulder, and collar etc move with the hand. You also have extra functions that show up on the Gizmo like Pinning. You can Pin say the foot so it stays put until you get to the extreme and then it will start to move.
7: Animate2: Never used this but obviously used for Animate2 Plug-in.
8: Surfaces Selection Tool: Allow you to select Surfaces in the Viewport. But with DS4/4.5 when an item is selected you can opt for just those surfaces related to that model show up in the Surfaces Pane. Or you can set the Surfaces Pane up to show any surfaces that is connected to that object like clothing for a figure. Or if you prefer showing all surfaces in a scene at one time then the Surface Selection Tool is for you. These Options can be found by clicking on the Pane Options Box, small striped square box at either the top right or left depending on what side your Panes are on.
9: Region Navigator Tool: When this is used you get the big yellow highlights when you hover over an item or part of in the Viewport Window (scene). This tool is connected with the Shaping Pane so it automatically selects the same body area in the Shaping Pane as you select in the Viewport.