SIMM stands for Single In-line Memory Module.  In SIMMs, the pins on the front and back are electrically connected so that they provide a single line of communication channel between module and the motherboard.  SIMMs generally come in 30- or 72-pin PCB.  These modules have a bandwidth transfer of 8 or 32 bits and were designed for use in very early PCs usually with up to 486 processors.  On Pentium classic and higher processors with 64-bit bus, 32-bit SIMMs should always be installed in pairs.  If not, additional memory will be ignored or the system may not boot at all.

DIMM stands for Dual In-line Memory Module.  In a DIMM, the opposing pins remain electrically isolated to form two separate contacts enabling a 64-bit data transfer.  This makes it possible to install modules individually.  Early DIMMs have 72 pins, but commonly they have 168 pins for desktop PCs and 144 pins for laptops.  Very recent processors, however, require faster transfer rate, hence the advent of DDR DIMMs.  These modules have 184 or 200 pins.  (See ff. links for relative information - SDR vs. DDR and SO DIMMs).

DIMMs and SIMMs are not designed to be interchangeable.  Their sizes are different and they install into different socket types.