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A function is a reusable block of code that performs a specific task. It is defined with the 'def' keyword followed by the name of the function and parentheses (()) containing any input arguments. Functions are beneficial because they promote code modularity and reusability, making it easier to manage and maintain the program. Here's a simple function in Python: ```python def hello(name): print("Hello, " + name + "!") ```

A module is a file containing a collection of related functions, classes, and variables, which can be imported into other files. Modules provide better code organization and the ability to reuse code across multiple programs. A Python module is a file ending with a '.py' extension, and it can be imported into another Python program using the 'import' statement. For instance, if there is a file called 'math_functions.py' containing some mathematical functions, here's how you would import and use one of its functions: ```python import math_functions result = math_functions.add(5, 10) print(result) ```

Based on the definitions and examples above, we can summarize the differences between functions and modules as follows: 1. Purpose: Functions are used to perform specific tasks, while modules are used to group related functions, classes, and variables that can be reused in other programs. 2. Structure: A function is defined using the 'def' keyword and has a set of input arguments and a return value (if applicable). A module is a file with the '.py' extension, containing a collection of related functions, classes, and variables. 3. Usage: Functions are called by their names followed by the input arguments within parentheses, while modules are imported into other programs using the 'import' statement. 4. Scope: Functions are limited in scope to the context in which they are defined, whereas modules can be imported and used across multiple programs. In conclusion, functions and modules play distinct roles in programming and help achieve better code organization, modularity, and reusability.