MAIN STYLES OF UPRIGHT PIANO
There are four main styles of upright piano: overstrung underdamper,straight strung underdamper, overstrung overdamper and straight strung overdamper. Here is a brief description of each:
Underdamper. All modern pianos are underdampers, which means that the dampers, which cut off the sound after the note has been played, are underneath the hammers. when looking down inside the piano from above, you can see the hammers with the dampers beneath them.
Overdamper. When you look down inside the piano, there is a plank of wood over the hammers, meaning that you can't see them easily.The dampers are above the hammers and are connected to the action with long cage-like rods. the damping is less efficient than underdampers,especially in the mid treble where the damper is too close to the top of the string to work efficiently. Most overdamper pianos, unless made by a top make such as
Bluthner or Ibach (both of whom produced many good ones), are not worth restoring if you want a good all round instrument.
Overstrung. Practically all new pianos are overstrung, which means that the copper bass strings cross over the steel treble ones.This means that the bass strings can be longer and therefore produce a deeper tone.

Straight strung There are many older, mainly British uprights that are straight strung.This means that the bass is weaker as the strings are shorter. However, some manufacturers made excellent straight strung pianos, notably Bechstein, Bluthner and Lipp, who deliberately designed the piano as a straight strung in order to produce a sweet tone and also to give an alternative cabinet style. The straight strung Bechstein model 10, for instance, has strings as long as the overstrung model 9 but a different style cabinet.

Illustrated is a straight strung underdamped upright with a half-plate iron frame.
MAIN STYLES OF GRAND PIANO
There are two main styles of grand piano: overstrung and straightstrung. Please see upright piano styles for an explanation. Only some pianos made before 1900 are straight strung.
GRAND PIANO ACTIONS
There are three common styles of Grand piano action: the normal roller action, the simplex action and the Bluthner patent action. These account for 99% of grand piano actions in pianos made from 1880; piano made before 1880 may however have a variety of different actions. Older Bosendorfer grand pianos (before 1890) often have "Vienesse" actions, which are not recommended.
Simplex actions
These are as the name implies, these are simpler than the normal roller actions found in over 90% of grand pianos. The most common firms that installed them are Challen and Monington and Weston (practically all Monington actions are simplex and about 40% of Challens). They are chosen as they take up less space and the piano can therefore be shorter. Firms making a large number of simplex actions made the touch feel very acceptable, though they are never as effective as the standard roller action and also tend to wear quicker. Other firms occasionally using simplex actions are Broadwood, Chappell, Lipp (rarely) and Allison.