Well, there is a certain dichotomy, just as a coin has two sides. Still, they are part of the same thing and there may be even something that connects both sides, being it the rim (on the surface) or the substance. Each side gives you a certain info about what we perceive as a coin.
Once you dig into ecology, you are being faced with a hard-on field of science, which can scrutinize on every form of organisational structures, may they be “natural” or man-made. I think both terms are nowaday loaded with a lot of clichés, for ecology being it the law of sustainability, whereas it is the mere attempt to describe natural organisational structures. And for economy the concept of being all about money and growth in contrast to its attempt to postulate laws of behaviour of individuals/groups. But as soon as we leave the clichés behind, the line that divides both fields becomes narrow. In fact so narrow, that our coin might actually become a ball. I have no hard feelings about the word “economy”, just about what people put into it (the same about “ecology”).