Inpatient treatment is any treatment required where it is necessary for you to occupy a hospital bed, either for the day (which is called ‘day-patient treatment’ or 'Daycase') or overnight.
As a hospital bed is required, this type of treatment often relates to more serious procedures. For example, if you were to require any kind of invasive operation this would almost certainly come under inpatient treatment (even if you only required the hospital bed for an afternoon).
Outpatient healthcare most commonly relates to specialist consultations and diagnostic testing. In other words, it often relates to the diagnosis stage of treatment.
For example, if you were experiencing chest pain your GP may refer you to see a Cardiologist, who would examine you and run a series of tests in order to identify the issue. Once a diagnosis has been made the Cardiologist may suggest surgery, which would then come under inpatient treatment.
Essentially, outpatient treatment relates to healthcare where you do not end up requiring a hospital bed or surgery.