**Core Concept**
The differentiation between follicular carcinoma and follicular adenoma of the thyroid gland is crucial for determining the appropriate management and prognosis. This distinction is often based on the presence or absence of capsular or vascular invasion, which are hallmarks of malignancy.

**Why the Correct Answer is Right**
The key to differentiating between follicular carcinoma and follicular adenoma lies in the histopathological examination of the tumor. Follicular carcinoma is characterized by the presence of capsular or vascular invasion, which is not seen in follicular adenoma. The diagnosis of capsular invasion involves the assessment of the tumor's ability to breach the capsule surrounding the thyroid gland, while vascular invasion refers to the tumor's ability to invade blood vessels. The presence of either capsular or vascular invasion is a strong indicator of malignancy.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because the presence of follicular cells with nuclear features of papillary thyroid carcinoma (e.g., ground-glass appearance, nuclear grooves, or intranuclear pseudoinclusions) is not a criterion for differentiating follicular carcinoma from follicular adenoma.

**Option B:** This option is incorrect because the presence of lymphocytic infiltration or Hashimoto's thyroiditis is not a reliable criterion for differentiating follicular carcinoma from follicular adenoma. These findings are often seen in both benign and malignant thyroid lesions.

**Option C:** This option is incorrect because the presence of a "Hürthle cell" component within the tumor is not a specific criterion for differentiating follicular carcinoma from follicular adenoma. Hürthle cells are a type of follicular cell that can be seen in both benign and malignant thyroid lesions.

**Option D:** This option is incorrect because the presence of a "papillary" component within the tumor is not a criterion for differentiating follicular carcinoma from follicular adenoma. Papillary thyroid carcinoma is a distinct entity that is characterized by the presence of papillary structures and nuclear features.

**Clinical Pearl / High-Yield Fact**
When differentiating between follicular carcinoma and follicular adenoma, it is essential to assess the tumor's histopathological features, particularly the presence or absence of capsular or vascular invasion. A thorough examination of the tumor's margins and the presence of any malignant features can help guide the diagnosis and management of the patient.

**Correct Answer: D. The presence of papillary structures and nuclear features of papillary thyroid carcinoma.**