In general, you have the following emissions from any fossil-fuel combustion process:
- Water vapour. This is virtually never harmful.
- CO2. This is not immediately toxic, but is a greenhouse gas, and net emissions must be reduced globally.
- Other combustion chemical products. Generally small fractions total emissions, though potentially hazardous to humans, including NOx (nitrous oxides), SO2 (sulfur dioxide), O3 (ozone), and trace pollutants such as mercury. All are bioactive or biotoxic.
- Physical emissions. In particular, fine particulate matter, essentially soot, most especially PM2.5 (2.5 micron particles). These are physical irritants and can contribute to lung injury and disease, among other factors.
Stating "ships emit X amount of pollutants" without specifying the pollutants is worse than useless, and often deliberately misleading.
Total CO2 emissions are wholly a function of the amount of fuel burned. Shipping is about 3% of total fossil fuel consumption, and hence, of total CO2 emissions. On net, and especially based on the total tonnage and value of goods moved, shipping is the most efficient form of transportation available. It is low polluting in terms of CO2.
Where ships trail, badly, is in particulate and chemical emissions. Ship fuel is "bunker oil", basically the last grade of petroleum above asphalt, and having a consistency when cold of tar or even a solid. Worse, it's also typically high in impurities, including sulfur, mercury, and other elements and chemicals. And when burnt tends to product high amounts of particulates. Given the regulatory environment, multinational, international waters, diverse, and often a race-to-the-bottom of bare minimum standards, marine emissions of these pollutants is high.
As a somewhat saving grace, these pollutants do tend to settle out quickly, and hence don't reside long in the atmosphere. Some, especially mercury, do reside in (and worse, bioaccumulate and concentrate) in life, which is why eating carnivorous fish (tuna, shark, swordfish) is not recommended.
But the full picture on shipping is that its pollutant levels vary greatly, compared to other sources, and in environmental impacts depending on the specific pollutants in question.