Those extra large grubs are the larvae of the ox or Elephant beetle (Strategus aloeus). The adults are large beetles and the males have 3 large horns on the hood-like body segment (known as the pronotum) behind their head. The following website shows photos of the male and female adults as well as the larvae and pupae.
The normal sized grubs we find in turf and gardens are larvae of June Bugs.
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