Inflammation vs. Infection
I may have written about this before, but the topic tends to be a sustained cause of confusion.
An eye can become inflamed if certain types of cells are redirected toward it from the rest of the body. These cells are often called inflammatory cells, which seems tautological in this context, but their presence really is the defining criterion of inflammation. The eye may also be red and swollen in association with an influx of these cells.
There are many different reasons that inflammation can happen. Sometimes we are unable to really identify the source of the inflammation. One common reason that inflammation can happen is invasion of a foreign microorganism–in other words, an infection. So inflammation can certainly result from infection, but not all inflammations are infectious in origin.