A shirt can be worn around the house, out in public, or for exercise. A suitable shirt already worn around the house for a day can also be used for exercise. Once it has been used for exercise, though, it cannot be used around the house or in public. The exception: cooling off for an hour or so at home before taking off an exercise shirt damp with sweat.
A shirt suitable for the house might also be suitable for public wear, later in the same day. By the same token, a shirt already worn in public can be worn the next day at home, but usually not on two successive days in public. A shirt worn briefly at home, before being exchanged for a shirt serving another function, can be worn the next day at home as well. Can it then be worn in public, too? It can, if free from stains and odors. There is a choice then: change to an exercise shirt, saving house shirt for later, or keep the same shirt on?
The overlap between exercise shirts and shirts for public usage is more substantial than might apparent at first glance. A clean, unstained exercise shirt is suitable for less formal situations, or for errands like getting gas or shopping at a hardware or garden store. In most cases, doing yard work or other outside chores will fall into the same category as exercising, and thus require a shirt with a similar function.