Let's ignore all trading - what is the relationship between settlements?
Let's assume that the asteroids are perfectly heterogeneous and there is zero material reason for them to trade with each other, what does the ship traffic look like?
It is highly unlikely that a single asteroid colony would be self sufficient, even over long term. You need replacement parts and things not manufactured on each individual asteroid. These things would come from Earth (Or Mars or someone other massive settlement of humans).
If there are 10 settlements, does Earth send 10 rocket ships with each settlements order? or does it send one to a central hub, which then on forwards the other 9 orders. For the same reason container ships don't stop at every minor town, supply rockets will have a similar hub and spoke arrangement.
Combine with this the transit time and cost of getting replacement parts from Earth, and your settlements will be exchanging rockets with parts and tools simply because it's faster and cheaper than relying on Earth if your neighbours have spares.
This means you have rocket ships between the settlements already, before you even factor in differing resources around the belt.
Now lets look at resources:
From Wikipedia's asteroid page:
The physical composition of asteroids is varied and in most cases poorly understood. Ceres appears to be composed of a rocky core covered by an icy mantle, where Vesta is thought to have a nickel-iron core, olivine mantle, and basaltic crust. 10 Hygiea, however, which appears to have a uniformly primitive composition of carbonaceous chondrite, is thought to be the largest undifferentiated asteroid. Most of the smaller asteroids are thought to be piles of rubble held together loosely by gravity, though the largest are probably solid.
So in short we don't know for sure, but it looks like composition is pretty varied. Your asteroid settlements will be probably trading raw materials.
However, look at more complex manufacturing. Does each colony need its own circuit board printing factory? Does each colony need its own IC manufacturing plant? Should each colony have its own chocolate factory? Trading allows for these specialist production facilities to be dispersed around settlements near each other in delta v costs, this is more efficient, and baring external factors like a war, is going to result in profitable trading for everyone.