In terms of the trains which clean the track, the ones which get rid of leaves and stuff on the tracks in Autumn/Winter are known as
Railhead Treatment Trains. (Railhead = the top of the rail, Treatment = they clean the track). They look like some blue tanks on wagons.
Going to the original few questions:
A
locomotive is a form of traction/motive power which is self contained. It's sole purpose is to move pieces of rolling stock around.
A
multiple unit is a form of coach which is self-propelled. They are either Electric (
Electric Multiple Unit, EMU) or Diesel (
Diesel Multiple Unit, DMU).
A
coach, often referred to overseas as "passenger cars", are the items of rolling stock which carry passengers.
A
wagon, often referred to as "trucks" or "freight cars", are the items of rolling stock which carry freight.
There are some differences between older and newer railway terms here: a "wagon" was more commonly referred to as a "truck" back in the days of steam but now the tables have turned - "wagon" is used more often.
The terms "coaches", "carriages", and "passenger cars" all mean the same thing.
When you get onto trainspotting, you need to know how the different engines, units, and coaches are classified. To be brief about locos and units:
British Rail introduced a system called the
Total Operations Processing System (TOPS) to classify the traction used on the railway network. This consisted of giving every engine and unit a number in a class. This had been done for years and years before BR, but TOPS brought it all to one centralised place. Essentially, say you have a Class 43 (a locomotive). The number would be:
43002
With "43" designating the class of the locomotive (Class 43), and "002" designating the individual engine number.
On the UK railway network, engines are given two-digit class numbers and units are given three-digit class numbers. The following system is used to designate unit numbers to classes and types of unit and engine:
It's probably also worth mentioning that sometimes the first number after the class number designates a sub-class number - engines or units with differences between batches, if you will, are given different sub-classes. Have a look at the Class 37s and Class 465s for examples - and the Class 66s - but with them you can be sat there for ages looking through all of them! 
"Departmental" units and engines are also a relatively common sight on the railway and are worth mentioning. They are essentially engines or units which have either been taken out of service for testing purposes or built to the specific requirements of a engine or unit for testing use. The Class 950 and 97 are good examples, the former being very similar to a Class 150 and the latter being a re-purposed Class 37.
I suppose it's worth mentioning that a Driving Van Trailer (DVT) is a item of rolling stock with a cab for controlling the locomotive at the opposite end of the train, but with no power source of it's own. The DVTs used on Chiltern Railways' Class 68 sets and LNER's Class 91 sets spring to mind as being examples of DVTs working with diesel and electric locomotives respectively.
I hope this helps in some way.
Thanks,
-Peter
