A logical database model is like a blueprint for how data is structured and related within a database system, without worrying about how it's physically stored. It defines the organization of data, how different pieces connect, and the rules that ensure everything works together smoothly. This model helps represent real-world entities and their relationships in a logical and efficient way.

For example, imagine Netflix managing vast amounts of data. For user profiles, they might use a document-oriented database like MongoDB. Here, each user's information—such as personal details, watch history, and preferences—is stored in a single document. This design allows for quick retrieval and updates, providing users with a seamless and personalized experience.

On the other hand, a social network like Facebook deals with complex relationships between users. They might use a graph database like Neo4j. In this model, data is organized as nodes and edges: nodes represent users, posts, and comments, while edges represent friendships and interactions. This setup enables the platform to efficiently query relationships, like suggesting friends or showing connections between users.

For applications needing rapid access to straightforward data—such as caching session information—companies might use key-value stores like Redis. Consider Amazon: their logical design uses keys to represent session IDs and values to store shopping cart contents. This allows for quick retrieval and updates, enhancing the user's shopping experience with fast and responsive interactions.

In big data scenarios like logging and analytics at Twitter, a column-family store like Cassandra might be used. This logical model organizes data into rows and columns within column families, optimized for handling large volumes of real-time data efficiently, especially with heavy write operations.

Logical database design tackles several important challenges:

1. Data Organization: Ensures data accurately reflects real-world entities and their relationships, making it intuitive and meaningful.
2. Data Integrity: Maintains consistency and accuracy across the database by defining constraints and relationships.
3. Performance Optimization: Aligns the data structure with how applications access data, improving performance and scalability.

Even though NoSQL databases differ from traditional relational databases, performing logical database design is still important and widely accepted. The main goal remains the same: to structure data in a way that effectively supports the application's needs.

Different types of NoSQL databases focus on different elements in their logical models:

1. Document-Oriented Databases: Use documents (like JSON or XML) and collections. The logical design focuses on how data is organized within documents and how documents relate to each other.
2. Graph Databases: Utilize nodes and edges to represent entities and their relationships. The logical model emphasizes the connections between data points.
3. Key-Value Stores: Consist of keys paired with values. Logical design involves structuring keys for efficient data retrieval.
4. Column-Family Stores: Organize data into rows and dynamic columns grouped into families. The logical model is tailored to optimize for specific query patterns and scalability needs.

In all these cases, logical database design is essential for building a data architecture that is coherent, efficient, and scalable, aligning perfectly with the specific requirements of modern applications.