Difference between precipitation and crystallisation
The two words are often used interchangeably (perhaps incorrectly), though there is a slight nuance.
IUPAC defines the following:

Crystallisation: The formation of a crystalline solid from a solution, melt vapour or a different solid phase, generally by the lowering of the temperature or by evaporation of a solvent.
Precipitation: The sedimentation of a solid material (a precipitate) from a liquid solution in which the material is present in amounts greater than its solubility in the liquid.

In essence, a crystallisation is the formation of a crystalline solid (i.e. not amorphous), for instance leaving a beaker of $\ce{NaCl}$ in water out for a long time will eventually grow crystals as the water evaporates.
Precipitation can be thought of a something 'crashing out', for instance if you have certain kinds of amines, you can add $\ce{HCl}$ in diethyl ether to precipitate out the $\ce{HCl}$ salt of the amine as they are not soluble.
There are of course in-between cases. Attempts at 'crystallisation' can yield amorphous solids if the conditions are not right, and, equally, precipitation can sometimes give crystalline solids.
The choice of words is therefore always ambiguous, but in general the IUPAC nomenclature should be followed where appropriate (eg. you can never crystallise to give an amorphous solid).
To answer the other part of your question about chemical vs. physical changes, you are correct that crystallisation is always a physical change (different isomorphs of the same material: amorphous, crystalline needles etc). Precipitation can be either, for instance in the $\ce{PPh3}$ case described by Jan, or in the $\ce{HCl}$ amine salt I previously described.