Applied Statistics and Mathematical Statistics are two branches of statistics that deal with the application and theory of statistical methods. Both branches are closely related but have different focuses and objectives.

Applied Statistics:
- Applied Statistics is the branch of statistics that focuses on the practical application of statistical methods in various fields such as business, economics, social sciences, engineering, and healthcare.
- It involves the collection, analysis, interpretation, presentation, and modeling of data to solve real-world problems and make informed decisions.
- Applied statisticians use statistical techniques to design experiments, conduct surveys, analyze data, and make predictions or recommendations based on the results.
- Some examples of applied statistics include market research, quality control, opinion polling, clinical trials, and risk analysis.

Mathematical Statistics:
- Mathematical Statistics is the branch of statistics that focuses on the mathematical theory and foundations of statistical methods.
- It involves the development and study of mathematical models and techniques for analyzing and interpreting data.
- Mathematical statisticians work on theoretical aspects of statistics, such as probability theory, distribution theory, statistical inference, and hypothesis testing.
- They develop mathematical models and algorithms for estimating parameters, testing hypotheses, and making statistical inferences.
- Mathematical statistics provides the theoretical framework and tools for understanding the properties and limitations of statistical methods used in applied statistics.

Both Applied Statistics and Mathematical Statistics are essential for a comprehensive understanding and application of statistics. While applied statistics emphasizes the practical aspects and real-world applications of statistical methods, mathematical statistics provides the theoretical foundation and mathematical rigor necessary for the development and evaluation of these methods.

Industry Statistics:
- Industry Statistics is not a branch of statistics but rather a specific application of statistics within a particular industry or sector.
- It involves the collection, analysis, and interpretation of data specific to a particular industry or sector to support decision-making and improve business performance.
- Industry statisticians use statistical techniques to analyze market trends, consumer behavior, production processes, and other relevant data to identify opportunities, optimize operations, and make strategic decisions.
- Examples of industry statistics include sales forecasting, demand analysis, customer segmentation, supply chain optimization, and quality control in manufacturing.

In conclusion, the correct answer is option 'C' because both Applied Statistics and Mathematical Statistics are branches of statistics that complement each other and are essential for the practical application and theoretical understanding of statistical methods. Industry Statistics, on the other hand, is not a branch of statistics but rather a specific application of statistics within a particular industry or sector.