Limited slip and locking differentials
A limited slip differential is a means to apply power to the ground when traction is limited, by sensing which wheel has traction and applying force to it, while maintaining the wheel speeds to be different when turning instead of only to the wheel that is without traction like how an open differential works.
How to tell an open differential from a limited slip differential (LSD)
Under normal conditions if the rear wheels are lifted off the ground and one of these wheels is rotated, an open differential will allow the rear wheels rotate in opposite directions. A limited slip (or "posi") differential will allow both wheels to rotate in the same direction, and it will be very difficult to hold one wheel from rotating while the other wheel is being turned. But a damaged open diff or a diff that has been converted by using a spool or mini spool, or a diff that has had the spider gears welded (an old school, dangerous "backyard" method to get two-wheel traction all the time) will ALSO allow both wheels to rotate in the same direction. Conversely, a LSD with a bent housing, worn clutches, or a galled pinion gears and/or cross shaft may not allow both wheels to rotate in the same direction with the rear wheels off the ground. Ironically, the way many open diffs get such damage is from extended spinning of the driven wheel.
Having both rear wheels spin under acceleration is not a positive indication of having a LSD. Under certain circumstances- like when rear wheel traction is identical for both rear tires- an open diff can behave like a LSD.
In some isolated cases like the second generation Pontiac Trans Am, a 10-bolt 8.5" corporate LSD rearend was standard equipment, so they will (except cars specifically ordered with an open rearend) have a LSD if it's original.
So, checking for a differential being limited slip or not isn't as simple as jacking up the rear of the car and turning the wheels, or seeing if both wheels spin when you hammer it. The only way to be 100% certain of what type of differential is in the rearend is to remove the cover (like in the case of a Salisbury-type rearend) or drop the center section (Hotchkiss-type rearend) and see what's inside.
Other ID cues
Rearend housings will often have codes stamped into the axle tube or center section (depending on make and type of rearend) that can be decoded to give the gear ratio, manufacturer, date of manufacture, LSD or open, etc. Some rearends can be identified as to type by the casting numbers (raised numbers cast into the metal, not stamped), because some rearends use different housings for open and LSD differentials.
Many posi rearends carried tags with info pertaining to the ratio and type of diff lube to use. This included tags that state to use limited slip lube only- a good indicator that the rearend was a posi originally, but of course this could have been changed during the life of the vehicle.
Different ways used to get limited slip
Limited slip is accomplished by different means, depending on the manufacturer, application and vehicle. There is the cone type LSD, there is the clutch type LSD, there are viscous type, there are locking type differentials (mechanical, pneumatic and electric operated) and all accomplish the same basic thing- applying power to the wheel having traction or basically both wheels simultaneously.
Depending on the type and application, there may be some slip allowed, i.e. the two wheels are not connected to one another directly, like in the case of the viscous, clutch, and cone types. In other cases (like the locking-type differentials), the wheels are directly linked while in the locked position.
A spool is not a differential, and isn't considered to be limited slip, either. A spool connects both wheels the same as if there were a live axle (think of a go kart from the '60s). In the case of a spool or mini spool (or welded spider gears), both wheels are turning the same speed all the time- even when going around a corner or doing parking lot maneuvers. This causes the inside wheel to rotate faster than it needs to when cornering or maneuvering. The result is reduced tread life, squealing of the tires even at slow speeds when turning, and a lot of stress on the rear end components. Not to mention a potential loss of control in low-traction conditions like ice, snow or rain.