Hi Chris,
Sorry about this it will be an essay but I hope it makes sense and helps.
HSS = High speed steel. A special tough, high carbon tool steel usually alloyed with cobalt (a metallic element, hence cobalt steels) which gives it high wear resistance. It is used for many tools including drills, milling cutters,lathe tools etc. It needs special high temperatures for hardening and tempering and will retain its cutting edge even when running red hot. It was the general; purpose tool steel until the advent of carbide tooling. It is also available as round or square sections to grind your own lathe tools etc but can be bought in preshaped sets for use on lathes etc.
TiN = Titanium Nitride a very hard ceramic used to coat tools, especially HSS tools to add extra hard wearing propertiess to the tooling, it is that gold colour you often see on milling cutters and twist drills these days. It is the same as titanium coating. because of its gold colour it is often used a coating in jewellery. Sometimes only the high wear areas such as the tips of drills are coated
Carbides are carbon based compounds which are very hard but brittle. They are mixed with metals, pressed into shapes and heated until the metal melts and cements the carbide particles together to form a very hard but less brittle matrix. hence its correst name is cemented carbide. The metal gives toughness to the matrix i.e. it is less brittle. Tungsten is often used hence 'Tungsten Carbide'. This is still quite brittle so small tips are brazed onto steel shafts which absorb the shock loads somewhat to produce carbide tipped tooling. Shaped tips which have several cutting edges are often used in lathe and milling tools and when blunted can be turned, or indexed and the next cutting edge used, they are held on a steel shank with special screws. Hence replaceable, indexible carbide tipped tooling.
Many folks use carbide tipped tooling these days but it was really intended for high speed, fast metal removal, production work, the fast removal shortening production times It is quite expensive (at least for me) but in production work the cost of tooling is negligible compared with production time and labour costs. It is not usually worth trying to sharpen carbide tooling,
I prefer HSS tooling for my lathe and mill as it is relatively inexpensive, easy to keep sharp and gives excellent finish on smaller lathes etc. It is easy to touch up and keep sharp once you have learned how to grind the angles, but as only a few basic shapes are required for the vast majority of the work we do this is not difficult.
Best regards
Terry