Snakum,
A spin is a stalled maneuver; no stresses are built up on the aircraft, no airspeed increase is experienced. In a developed steady state spin, the aircraft motion varies but the forces which lead to the spin keep it in the spin until outside inputs are made to stop rotation and break the stall (reduce angle of attack).
In a graveyard spiral, airspeed is increasing, the wing is not stalled, and typically the spiral is initiated and caused by the pilot. The pilot sees a dive and keeps pulling back on the yoke or stick, tightening the turn and making it worse. As the aircraft rolls into a steep descending turn, forces rapidly build up until ultimately the aircraft can come apart in flight (usually due to pilot inputs, but it can happen spontaneously on it's own if left in the spiral). The primary difference between the two is the stalled condition.
The feeling between the two is very different, though the sight picture is similiar. The biggest instrument indication difference is the airspeed. In a spin, the airspeed will stay put, bouncing the needle at the stall, or even zero reading. In a graveyard spiral, the airspeed is increasing, and will push toward redline quickly. If airspeed is increasing, you're not in the stall or the spin...you're in a dangerous situation. Get the power off, level the wings, and make a slow, steady recovery to avoid a high speed (accelerated) stall...which will often lead to some violent maneuvering.
The feeling in the spiral is one of being pulled into ones seat; acceleration or G forces build rapidly, and it's obvious. If you were filming it, you'd find that quickly a handheld camera would be dragged down and end up pointing at the panel or the floor of the cockpit. Your head tends to do the same thing, and your sight follows. If you feel your chin tucking, you are probably not in a stalled, spinning condition.
In a spin, you don't have this sensation. You will generally have a strong awareness of rotation, unless you're already disoriented and on instruments (in which case determining the direction of spin may be impossible). In the spin, you'll feel the tail of the aircraft sliding behind you, and the nose rotating in front of you; you'll likely feel as though the aircraft is rotating around you. A spin is a coupled yawing and rolling motion which is continuous, but not linear; it rotates faster and slower and goes through "phases" of the spin. It changes pitch, and may roll inverted, or flatten out in cycles.
In the spiral, you feel as though you're turning. You feel the nose moving into the turn, but you don't have the same sensation that the tail is rotating around behind you. I wouldn't rely on this as a determining factor (look at your airspeed), because by the time you analyze the event to this degree, you've gone too long. As soon as you see the airspeed coming up and realize you're in a nose low descent and a turn, reduce power to idle, identify your aircraft pitch and roll attitude, level the wings, and increase elevator and pitch trim nose-up as required; treat it as an overspeed recovery and do it gently.
I hope that helps.