Do TerraGo GeoPDF documents use a special or proprietary format?

No. TerraGo GeoPDF documents are PDF documents which conform to the PDF specification governed by ISO 32000. There is some confusion about how the georegistration information in a GeoPDF document, however. TerraGo invented the georegistration of PDF documents and released the specification to the Open Geospatial Consortium (OGC) to be published as a best practice. Adobe also promulgated, in cooperation with TerraGo, a separate georegistration specification which has been incorporated into the ISO specification that governs PDF ISO 32000. It is the author’s option in TerraGo to choose either encoding.