Final answer:
The two types of branching of exocrine glands that the question refers to are Merocrine and Holocrine secretion. Merocrine glands secrete via exocytosis without cellular damage, while Holocrine glands release secretions by rupturing secretory cells which then become part of the secretion.
Step-by-step explanation:
The two types of branching of exocrine glands are Merocrine and Holocrine secretion. Merocrine secretion involves exocrine cells releasing their secretions without any loss of cellular material, often through a process called exocytosis. An example of this would be the eccrine sweat glands. In contrast, Holocrine secretion is characterized by the complete rupture and destruction of the secretory cells, which then become part of the secretion itself; this is seen in glands like the sebaceous glands of the skin.
Exocrine glands function to release their substances through ducts that lead to the surface of an epithelium rather than directly into the bloodstream as endocrine glands do. This system includes a wide variety of glands including mucous, sweat, and salivary glands, which help in various physiological functions like digestion, temperature regulation, and lubrication of body surfaces.
To further clarify the other options provided by the student's question: Apocrine glands are similar to merocrine glands but include the loss of the apical portion of the cell during secretion. Simple and Compound refer to the structural organization of the gland's duct system, not to the method of secretion. Endocrine and Paracrine are classifications of glands based on their target cells, but do not pertain to branching of exocrine glands.