Occupational therapy is more focused on daily activities such as washing their hair, getting dressed, cutting food, lifting a cup of water.
Occupational therapy is strength, endurance, flexibility, balance as they relate to activities of daily living. Brushing teeth, cooking, eating, bathing, grooming etc. Occupational also extends, at times, to instrumental activities of daily living such as driving, working, shopping etc.
They both deal with function. In may cases, arms go to OTs, legs go to PTs. This is not the design, but the reality. You will work together to increase total function. PT contributes to ADLs and IADLs, but would never set a specific goal for grooming or dressing. OTs would never set a goal for just physical improvement without it relating to a specific task.
The relationship should never duplicate services on the same patient, but this is a gray area. The reality is that transfer training to increase ability to brush teeth, is the same as transfer training used to increase efficiency and allow for better general mobility. I hope this helps.