Mike is correct in that PTIs wore crossed swords as their TB. It is one of the oldest trade badges in the British Army thus the Canadian Army. Originally, the badge was created for swordsmanship awards to get soldiers to keep up their skills; it evolved into a a skill-at-arms badge and then into PT instructors
Crossed axes is the badge of the Infantry Pioneer soldier who built bunkers, laid mines and barbed wire and booby traps defensively and cleared enemy mines and barbed wire and booby traps when their unit moved onto the objective. The Pioneer section was usually small because the men who actually did the work would be the infantry soldiers under pioneer supevision.