Residents of a settlement may trade goods and services with other residents within the settlement. As the settlement grows larger, it may change from some kind of centrally run organization into a complete society with all imaginable commercial services. As the population diversifies, skills will also vary, and children and older adults may find time for activities that have commercial aspects. Due to the wide gap in costs between locally produced goods and imported goods, there may be many opportunities for local entrepreneurs to develop products and services for commerce.
People on Mars will probably still be earning money on Earth. All of a settlement's initial population needs to come from Earth, and they will own properties on Earth that generate revenue that they will spend on Mars. Settlers will import equipment than can transform basic in-situ produced resources into goods, and the gain in value will have a trading value. Settlers will apply their intelligence to improve processes, refine products and find new uses for existing goods; and again, the gain in value will have a commercial value.
Although a Martian settlement will have strong energy and agricultural sectors, these will be highly automated, as on Earth. These will therefore not represent the largest part of the work, that will mostly be in the form of services, again, as on Earth in developed economies.
Artwork and craftwork
Artwork helps improve morale and may provide individual income. Craftwork made from ceramics, biomass (weaving, cloth making, paper) and 3D printed items as well.
Due to transportation costs, practically anything made on Mars will be less expensive than the same item imported from Earth. This allows for a tremendous amount of local trade, in particular if there is capital from Earth that can be used to pay. Sponsoring organizations and Earth based corporations will take every opportunity to reduce their costs by using local products.
Electric power may follow the utility model, but it might also be a private service. Prepared foods take time, and restaurants or caterers can provide them. Vehicle may also be public, or private. Private ownership of advanced 3D printers could create a trade in any number of consumer goods and in the maintenance and repair of them. Clothing is also a type of goods that could be traded, all the way from underwear and socks to spacesuits.
Any improvement of a material, transforming iron into steel, steel into structural elements, structural elements into finished goods will have value and can be traded.
Hairdressing, medical services, decoration, teaching and coaching. Food preparation and nursing. Public services, daycare, legal services, recreation and entertainment, volunteer work.
On a larger scale, service sectors such as finance, real estate, engineering, commerce and tourism will probably provide the largest amount of work on Mars, and as the settlement grows will become the dominant part of the economy. Many of these are delocalized and can be traded electronically, without physical movement between the settlements.
Automation will provide very high individual productivity as long as the available energy is high.
In his "Mars Trilogy" novels, Kim Stanley Robinson had multiple economies on the developing Mars. Oxygen and goods (which could be built anywhere) used normal commerce, but Nitrogen (which was only available in very limited areas and was vital to life support) was distributed via a gift economy.