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I've found in many articles that GPS devices use the spheres theory to get the its position, but sometimes I read that these devices solve for time differences between satellites transmissions, using hyperboloids.

I want to understand which one is correct?

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They use both. Spheres are around each satellite. The intersection of 2 spheres (from 2 satellites) with a certain difference in radius results in a hyperboloid. 3 satellites result in 3 spheres, 2 hyperboloids that result in a curved line. 4 satellites result in 4 spheres, 3 hyperboloids, 2 curved lines and when those 2 lines intersect you get a point = your position! All signals received and calculated by a small gadget in microseconds.

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