Good question. Field Companies and Field Squadrons are close to
the same thing. Field Companies were attached to Infantry Brigades/
Divisions and Field Squadrons were attached to Armored Brigades/
Divisions. The differences were slight.

Park Companies/Squadrons were plant oriented units with heavy
equipment and tradesmen. Plumbers, Fitters, Carpenters, Electricians
etc were placed in Park Company.

Hope this helps.

My knowledge comes from History of The Royal Canadian Engineers Vol II.

By my reading, it would appear that the Field Companies were designed to
carryout "heavy" engineering tasks, such as more permanent bridges and roads etc.

There were quite a number of specialist units such as Tunneling and Petroleum Companies.

Hope this helps.

Chimo