This is the biggest difference (quote from semver.org):
"Major version X (X.y.z | X > 0) MUST be incremented if any backwards incompatible changes are introduced to the public API. It MAY include minor and patch level changes. Patch and minor version MUST be reset to 0 when major version is incremented."
Meanwhile the PVP lets you get away with just updating the minor version there.
Oh, I realize that PVP does not require everything semantic versioning does. It sounds like PVP requires nothing semantic versioning forbids, nor vice-versa? In which case, you could (and, I would assert, should) follow both.
"Major version X (X.y.z | X > 0) MUST be incremented if any backwards incompatible changes are introduced to the public API. It MAY include minor and patch level changes. Patch and minor version MUST be reset to 0 when major version is incremented."
Meanwhile the PVP lets you get away with just updating the minor version there.