According to the lore, it's the small ship FSD that is based on Thargoid tech. The lore isn't totally clear but it's implied that megaships are using an older jump technology that predates Sirius Corp's commercialization of the FSD, presumably because the ship FSD is impractical to scale up to such high hull masses. Correspondingly, the visual resemblance of megaship jumps to Thargoid wakes is somewhere between coincidental and due to the fact that both are making use of the Witchspace dimension.
Edit to add a note about FSD scaling:
We don't know the hull mass of a megaship. However, the dedicated large cargo ship (T9) achieves a cargo mass fraction of 90% (790T in an 850T hull) or almost 100% if you count the fuel tank. If we assume the same of fleet carriers they must have a hull mass of at least 25 kT. FSD optimal mass doesn't increase linearly with size, but the largest three sizes go up by about 50% per level. If that scaling held true (it might not) you would need about a class 13 FSD to move a fleet carrier. Meanwhile, they are clearly getting exponentially harder to build as you scale up - the cost increases by about a factor of three per class at the larger sizes. If that trend continued, a class 13A FSD would cost 37 billion credits - far more than the carrier itself! (If FCs use lowly C-rated drives, then the math kinda works, as a class 13C FSD would cost 3.7 billion, although that doesn't leave much margin for the rest of the bill of materials. Although more likely the math is actually much worse, as you need an optimal mass of more like 200 times the ship mass to get the range up to 500 LY, which means an unimaginable class 26A FSD!) Point being, it's at least logically consistent to suppose that ship FSD tech doesn't scale up to megaship scale.