Technically, there is only one seam on a baseball.
The covering of a baseball is made up of two interlocking swaths of white horsehide (affiliate link) or cowhide, each shaped like an oblong figure 8.
The two pieces are sewn together using 108 threaded stitches (usually red, blue, or black), forming one continuous seam traversing the sphere.
This notation actually refers to the number of times a pitcher’s fingers, thumb, or palm cross the single seam, and where, as he holds the ball and delivers his pitch.
A two-seamer, for example, is held with the index and middle fingers gripping adjacent sides of one looping end of the seam, with the thumb inside the other loop, touching only the leather hide.
So, while the fingers, thumb, or palm can use different parts of the stitching to achieve desired results, there remains just one continuous, looping, round-trip seam on each baseball.