Dogs do have a different sense of time because they do depend largely on smell.
However dogs also perceive time differently as they don't understand clock time or the calendar time like us humans do.
Dogs do not understand clock time or calendar time in the same way that we do, but they do have some perception of the passing of time that is unique to them.
While sense of time has not been as widely studied as other areas of canine cognition, a few key studies have been done.
Dogs usually perceive time through their smell as different parts of the day smell different to the dog depending on the time of day.
To dogs, time quite literally smells different throughout the day.
Morning has a different scent from afternoon, which smells different from night-time.
The canine nose is so sensitive that dogs can determine the difference between 5:00pm and 6:00pm, the time when your partner's car rolls into the driveway every weekday.
Research indicates that it's quite likely that a dog's sense of smell can pick up fear, anxiety and even sadness.