Case:
Watch cases can be distinguished by material, size and shape.
Materials (by increasing hardness):
Plastic, Brass, Aluminium
Gold, Silver, Platinum, Palladium, Rhodium
Titanium, Steel, Ceramic
Size: 10-50 mm, gents ø>35 mm, ladies´ ø<30 mm
Shape: round, square, rectangular, trapezoid, tonneau

Platings/Coatings: Soft (e.g.brass) or unprecious base materials (e.g. steel) are upgraded by precious (gold) or harder (Titanium) materials. The thickness is measured in mikron = µm = 1/1000 mm. Physical procedure with pressure and temperature (PVD - Physical Vapour Deposition) is distinguished from anodizing/acid/electrochemical/galvanic plating.
Anodized platings are 5-60 Mikron thick - the thicker the more wear resistant.
PVD platings (Cathode atomizer) done with Titanium Nitride, Titanium Carbid or Wolfram Carbide with platinum or gold inlays are up to 20 times harder and more wear resistant, therefore only a thickness of 0.5-2 micron is needed.

Case back:
Snap-in back costs less, but the max. water resistance achieved is 50 meters.
Screwed back protect the inside of a watch better against dust and humidity. Can be identified by an outer ring of litte notches to set on an opening tool.
Display or glass backs of mineral or sapphire visualize the mecanical movement. Inside an automatic watch, one can see the rotor.

Movement:
The movement is the "motor" and the pivot point of the whole watch, its size and functions determine watch size and design (e.g. additional crowns or pushers), dial layout (e.g. arrangement of hands, day/date indication, timezone indications, subdials etc.) On many watches on can conclude the movement behind from the dial layout alone. Main requirements are accuracy and shock resistance.
Quartz movement is an electronic movement, normally with a battery as energy source. It is extremely accurate with deviations of merely a few seconds per month. A quartz movement is obviously inside the watch if it has a "jumping" second hand.
Mechanical movements have a sweeping second hand. The manspring serves as power resource. Despite of highest fine mechanical precision, it it the nature of mechanical watches that the interaction of mechanical parts does always lead to some inaccuracy, in fugures usually a few seconds per day at least. The power reserve of a fully wound mechanical watch is around 2 days.
Automatic: The movement of the wrist moves a rotor which winds the mainspring "automatically"
Manual wind: No rotor, i.e. it has regularly to be wound manually through the crown.
Hybrid: Combination of Automatic and Quartz - a mechanical rotor energizes a generator-condensator-system providing energy to a quartz movement. Power reserves of up to 100 days are possible. Brand names are Seiko Kinetic or ETA AutoQuartz.

Jewels are the bearings for rotating mechanical parts in a movement. Quartz watches with only a few rotating mechanical parts have maybe 5 jewels, mechanical watches have about 17-50 depending on the complication. The number of jewels doesn´t say anything about the quality of a movement.

Dial and Hands:
Analog indication with indexes and hands
Digital indication with figures - normally only in combination with quartz movements.
Illuminous Tritium paint on dial indexes and hands is usually indicated by the the impring T or T25 on the dial.
Day/Date indication can be available in different languages.
Complications are additional functions of a watch, e.g. timing functions of a chronograph, these are usually indicated seperately on subdials.
Hands are available in numerous shapes, Baton, Dauphine, Breguet, lance, skeleton, etc. How the second hand moves allows concluding the type of movement behind the dial: A jumping second hand has a quartz movement behind, a sweeping second hand a mechanical movement.

Crystal:
Crystals must be scratch and shock resistant. The harder and more scratch resistant, the less flexible and shock resistant is a crystal. Hardness is measured on the MOH´s scale in steps from 1-10 (Fingernails = 2, Steel = 5-6, Diamond = 10). The classification is according to which material scratches another.
Sapphire, artificially manufactured material, MOH 9 = next to diamond, extremely scratch resistant.
Mineral glass with hardened surface, MOH 6-7 = still harder than steel.
Plastic/Acrylic glass = PMMA = Polymethylmethacrylat, MOH 3-4, less scratch, but more shock resistant and scratches can be polished out with special acrylic polishes. Also the right material for extremely domed crystals.

Water Resistance:
Waterproof means only protected against sprinkle water, not for swimming.
Water resistant means testet for 30 min. (30m) in 1m depth and 90 sec. in 20m depth. 30m does not mean 30 meters, but 30 minutes and is used quite misleadingly by the watch industry in this contents because such watches are not even suited for swimming, showering etc. For swimming the watch should have 50m/150 ft and for diving 100m = 100 meter/300 ft or more.
Screw crown and case back ensures extreme water resistance, always screw these parts tight, but not overtight to prevent seals from being squashed.

Band:
Watchbands are distinguished by materials and band width.
Leather-, rubber- or textile straps are cheap, comfortable to wear and easy to adjust in length for different wrist sizes. Leather (exception Aqualeather) is hardly water resistant. Straps do mostly come with tang buckles.
Metal bracelets are more rugged, durable and water resistant. Normally they are adjusted in length to fit a certain wrist size (special tools needed!).
Quality features:
Solid, screwed links
End link also solid
Buterfly clasp with pusher release
Band widths are available in steps of 2 mm from 10-24 mm, often the band is narrowing down by 2 mm from the case to the clasp.

Chronograph vs. Chronometer:
Chronograph: Watch with time stopping functions, usually indicated on small subdials.
Chronometer: Very accurate mechanical watch having passed an accuracy test at the independent Swiss Control Agency "C.O.S.C" (Contrôle Officiel Suisse de Chronomètres). The movement is tested in different positions for up to 2 weeks and it´s accuracy does not exceed - roughly said - about +/- 5 sec. per day, it gets the COSC certificate. On Quartz watches, this test does not make much sense since it´s their nature not to exceed a few sec. per month in accuracy.