Oh, happily.

Interleukins are a great example, as a class. They were first discovered as signaling molecules between white blood cells (inter-, -leukins, leuko meaning 'white'). Unsurprisingly, though, just because we found types of cell-cell communication in immune cells first doesn't mean it's unique to the immune setting. Some examples:

Interleukin-1 acts as a neutrophil chemotactic agent. It attracts that group of immune cells. However, it also acts to regulate the differentiation of osteoclasts. Osteoclasts are the cells that break down bone. They're a normal part of bone physiology - bone is constantly being broken down and rebuilt, as part of the normal bone remodeling process. If this were discovered by cell biologists before immunologists, it would've been named something like "osteoclast differentiating factor". Sometimes it goes in the other direction: what was originally named "osteoclast activating factor" was ultimately renamed Interleukin-1Beta.

Interleukin-4 is primarily known for its role in regulating B-cell differentiation.. It was one of the earlier lymphocytotropic hormones fully characterized and reproduced in the lab by immunologists. However, IL-4 receptors have been found on numerous cell types, strongly suggesting its pleiotropy: human myocardium expresses an IL-4/13 type II receptor, which allows it to respond to IL4 and IL13 signaling. Lab studies suggest that this allows IL4 and IL13 to jointly regulate human heart muscle contractility and baseline metabolism (knockouts for IL-4 and IL-13 receptors have shown impaired contractility and dyssynergic heart contraction.) You can imagine if this had been discovered by molecular biologists before immunologists, this would have simply been a "myocyte regulatory factor 3" rather than "interleukin 4". There's no immediately obvious immunologic connection, outside of the broader umbrella of homeostasis (stress conditions -> inflammation, stress conditions -> increased cardiac activity.)

Moving away from the interleukins:

Tumor Necrosis Factor-alpha is a major immune/inflammatory regulatory; it plays a key role in the acute response to sepsis, induces apoptosis and cachexia, and is produced chiefly by various immune cells. It's also expressed in taste bud cells where it modulates neural responses to bitter tastes. Overexpression = stronger response to bitterness. It's postulated that this is why severely inflammatory states may be associated with taste distortion. No one really cares that much about physiology of taste, so even if the immunologists had been last to the party, we still would've ultimately classified this an inflammatory mediator.

And these are the obvious ones. There are more subtle ones, like macrophages and their associated matrix metalloproteinases. These are involved in tissue remodeling and thus wound healing, and thus kind of obviously fall under the broad heading of "inflammation," since we associate pretty much anything even vaguely related to trauma as "inflammatory." But really, remodeling extracellular matrix happens constantly in healthy tissues and is part of normal physiological activity. If I'm not mistaken, matrix metalloproteinases weren't discovered in the immune/inflammatory setting first - they were discovered as part of general cell biology.