Does a full-thickness tear of the achilles tendon mean a complete rupture? or does it mean that there is a tear going though the entire tendon depth?

Not necessarily: Rupture is just that it is no longer attached but you can have a full thickness tear but still have some connection at a different point. Ask the doc who ordered the scan.

Semantics.: To me both descriptions are one in the same. There can many ways to describe the same injury, often based on personal preference and what would most easily be understood by a patient.