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From the PRD:
"Burst, Emanation, or Spread: Most spells that affect an area function as a burst, an emanation, or a spread. In each case, you select the spell's point of origin and measure its effect from that point.
A burst spell affects whatever it catches in its area, including creatures that you can't see. It can't affect creatures with total cover from its point of origin (in other words, its effects don't extend around corners). The default shape for a burst effect is a sphere, but some burst spells are specifically described as cone-shaped. A burst's area defines how far from the point of origin the spell's effect extends.
An emanation spell functions like a burst spell, except that the effect continues to radiate from the point of origin for the duration of the spell. Most emanations are cones or spheres.
A spread spell extends out like a burst but can turn corners. You select the point of origin, and the spell spreads out a given distance in all directions. Figure the area the spell effect fills by taking into account any turns the spell effect takes."
So, basically, you pick your point of origin, and it covers every space that could be reached along some 20 ft path from that point, not only straight lines from that point. In many cases, you can treat it just like a burst effect, since being a spread only makes a difference when there are actually corners to turn within 15 ft of the origin of the spell.
As for additional saves, I have no idea what the spell does, so I can't help you there.
Spread vs burst
Spread does not need line of effect, whereas burst does. You can be behind a corner and avoid a fireball (burst), but an entangle (spread) will still grab you. Think of spread being like if it were smoke or water. It will flow around obstructions. Burst are more of direct hits coming from an origin that needs to have a line going to the target.
what about the vertical, can black tencatles (Area 20-ft.-radius spread) grab someone 20ft in the air?
If they are inside the 4 squares above the origin, yes. 3D combat gets a little more tricky, as you are dealing with a 20ft sphere on a normally flat combat map. This is purely assuming all spreads are spheres.
Editing this, as the rules are written with a flat map in mind. Entangle and Black Tentacles are ground surface emanations in concept (not explicitly RAW), so it would be a GM call or FAQ. Entagle I can see being environment dependent. If you were in a forest, I would go for a sphere. If you were in a field, I would say that grass is not reaching up 20 feet. Black tentacles is also another matter. How long are the tentacles, and can they reach up 20 feet