What is the difference between monoecious and homothallic?
The difference is that they come from different scientific traditions and describe the same idea for different kinds of organisms. Homothallic is applied to fungi and algae, whilst monoecious is applied to plants (and sometimes invertebrates). This use of different words to describe the same phenomena in different types of organisms is unfortunately quite common. You could also had hermaphrodite as another example for organisms with both male and female reproductive parts. One can point to crude phenotypic differences to justify the distinction in terms but the underlying concepts are the same.

I note as well that the separation into different types of organism used is usually based on older classification systems rather than reflecting any biological reality.