**Core Concept**
Carcinoid tumors are a type of neuroendocrine tumor that arise from neuroendocrine cells, which are specialized cells that produce and secrete various hormones. These cells are found throughout the body, particularly in the gastrointestinal tract, lungs, and pancreas.

**Why the Correct Answer is Right**
Carcinoid tumors develop from neuroendocrine cells that are part of the diffuse neuroendocrine system. These cells are characterized by the presence of neurosecretory granules, which contain hormones such as serotonin, gastrin, and vasoactive intestinal polypeptide (VIP). The production of these hormones by carcinoid tumors can lead to a range of clinical symptoms, including flushing, diarrhea, and wheezing. The most common site of origin for carcinoid tumors is the small intestine, particularly the ileum.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because carcinoid tumors do not develop from adenocarcinoma cells, which are the cells that give rise to more common types of gastrointestinal cancer such as colorectal cancer.
**Option B:** This option is incorrect because carcinoid tumors do not develop from pancreatic islet cells, which are responsible for producing insulin and other hormones.
**Option C:** This option is incorrect because carcinoid tumors do not develop from thyroid C cells, which produce calcitonin.

**Clinical Pearl / High-Yield Fact**
It's essential to remember that carcinoid tumors can produce a range of hormones, leading to a variety of clinical symptoms. A high index of suspicion is necessary to diagnose these tumors, particularly in patients presenting with flushing, diarrhea, and wheezing.

**Correct Answer: D. Neuroendocrine cells.**