A relay switch is composed of an electromagnet that actuates a high power switch made of two metallic contacts. Thus a very small current current that supplies the electromagnet coil, closes the power switch which is placed in series with a second high voltage, high current circuit. Both the electromagnet and the contacts are packed together in a single case (usually made of plastic material) (having the dimensions of a half of a match box).
A reed switch is composed only by the contacts themselves that triggers the conduction in the secondary circuit. Usually these contacts are made up of already magnetised metals, such that when an external magnetic field is applied the switch closes. Only the contacts are packed in a small glass cylinder (usually of a few mm^3, like a tiny resistor). The external magnetic field is supplied by an external permanent magnet or by a coil that is wrapped around the glass package by the person that uses the reed switch. Because reed switches are much smaller than relays usually they are used to drive lower power secondary circuits than relays.