SPD = Shimano Pedal Device - Shimano developed the clipless MTB pedal. and SPD aka Spuds tends to get used as a general term for clipless pedals (which itself is a stupid term as you are clipped in!).
fyi - most road/tri riders use "standard" clipless pedals such as those from Look, Shimano, Speedplay, Time etc. the cleats are large and when on the shoe they do make it more difficult to walk in.
but roadies tend not to walk as much as mountain bikers - terrain issues - so to make MTB shoes easier to walk in Shimano developed the SPD system with smaller, recessed cleats and ridge soled shoes for extra grip when walking off-road.
the KEY differences are:
- road cleats and shoes are stiffer (carbon or glass fibre soles)and allow more pressure through the pedals so increased speed
- MTB shoes have softer soles for walking so aren't as stiff so do not transmit so much power through the pedals
that's why you end up having 2 types of shoe - one for road, one for MTB. but many will use MTB cleats on both so they don't need different shoes but you'll rarely see a road pedal used off road due to the walking issues