How did you get on? Did you manage to write anything down before you looked it up?
Here are my thoughts
Underway: not anchored, or made fast to the shore, or aground.
Making way: being propelled through the water by sail, machinery or oar.
This is easy to distinguish by day because of the various day shapes used, but at night you must be able to decipher the lights displayed for information:
Special Lights - indicate the type of vessel eg Not Under Command (NUC), Restricted in Ability to Manoeuvre (RAM), Constrained By Draught (CBD), Fishing.
RAM, Fishing and Trawling vessels are underway when they show their special lights, and making way if they also show masthead, side and stern lights.
Not Under Command vessels show side and stern lights, but do not show masthead steaming lights when making way. They may have engine or steering trouble, so may be erratic in their course and speed. A steaming light indicates ‘proceeding under engine’, and direction of travel, both of which may be misleading for NUC vessels.
Tugs can be defined as towing when they show towing lights.
Motor, Sail, Tugs and Constrained by Draught, always show special lights if required, side and stern lights along with masthead steaming lights.
Pilot vessels show side and stern lights and their special white over red lights.
All these vessels can only be determined as under way at night and for 99.9% of the time they will actually be making way, but you cannot assume that.
The reason for the different treatment is that certain vessels may or may not be making way by virtue of the work they do - such as dredgers, survey vessels and cable layers. Fishing vessels may drift with nets out, or make way towing nets or trawls. Vessels Not Under Command may have operational engines - or not. It is important to separate all these situations because it would otherwise be uncertain what the vessels may do and you need to decide on appropriate actions.
In restricted visibility, a motor vessel makes different fog signals:
1 long blast every 2 mins when making way
2 long blasts every 2 mins when stopped - i.e. not making way