The main difference between Apache Spark and Hadoop MapReduce is that Spark can cache data in memory, making it much faster for iterative algorithms and interactive data analysis. Additionally, Spark offers a broader range of APIs, allowing developers to work with data in various formats like SQL, streaming, and machine learning. On the other hand, Hadoop MapReduce provides fault tolerance through data replication and is better suited for batch processing and large-scale data processing.

Apache Spark and Hadoop MapReduce differ in their approach to data processing and execution. Spark uses a directed acyclic graph (DAG) engine that optimizes the execution plan based on the data and operations involved. This enables Spark to perform in-memory processing, resulting in significantly faster performance compared to MapReduce, which relies on persistent disk-based storage. Furthermore, Spark provides a more intuitive and developer-friendly programming model, offering APIs in Java, Scala, Python, and R, while MapReduce is primarily Java-based.