What you call sandals the Romans called boots. Their boots were open on the top but still heavily soled. This suited their climate and kept the foot cool and dry.
So maybe they were both
(If I were to see someone wear them today, I would call them sandals)
The closest in terms of function would probably be the jungle boot, where the uppers have drains and fabric air circulation panels built in to keep the foot cooler and dryer.
These boots were designed to allow the wearer to walk long distances without discomfort in the Mediterranean climate of the Roman empire