Dynamic heterogeneity in supercooled fluids is often Monitored using four-point structure factots. We show that a four-point structure factor slightly different from the one commonly used reveals the :existence of large and long-range dynamic correlations, which dominate the correlations identified with dynamic heterogeneity. Specifically, we compare two four-point structure factors that differ by the mobility field used in their definition. The mobility field used in our alternative four-point structure factor, which we denote as S-4(F)(q, k; t), is the full microscopic self-intermediate scattering function, whereas the mobility field in the structure factor commonly used to examine dynamic heterogeneity, which we denote as S-4(cos)(q, k; t), is is the real part of the microscopic self-intermediate scattering function. The Susceptibility chi(F)(4)(t) and the correlation length xi(F)(4)(t) associated with S-4(F)(q, k; t) are both much larger than the susceptibility chi(cos)(4)(t) and the correlation length xi(cos)(4)(t) associated with S-4(cos)(q, k; t). In particular, we find that xi(F)(4)(tau(alpha)) grows proportionally with the relaxation time, xi(F)(4)(tau(alpha)) similar to tau(alpha) while we previously established that xi(cos)(4)(tau(alpha)) has a much weaker dependence on the telaxation time. We argue that the growth of xi(F)(4)(tau(alpha)) is primarily due to the growth of a transient elastic response, while the growth of xi(cos)(4)(tau(alpha)) is due to spatially correlated domains of slow and fast particles, usually referred to as dynamic heterogeneity.