What are the differences between these two database structures?
ER diagrams document business rules. They are a visualization of many subject-verb-object sentences. Take the classic shopping cart example. Some rules may be


A customer places one or more orders.
An order consists of one or more items.
Each item is a purchase of exactly one product.


The nouns become entities (boxes in the ERD) and the verbs relationships (ERD lines and arrows or crows feet).

Your two diagrams represent different sets of business rules. For example, on the left there is no link between roster and case. The diagram is stating that, in the particular situation you are modelling, your users consider rosters and cases to be completely independent; neither places any constraint whatsoever on the other. The right-hand diagram, however, has a relationship between them. This states a case is somehow linked to a roster. The relationship name will document what that link is.

Because they are linked the right-hand system will be able to answer a whole class of queries the left-hand one cannot e.g. "which cases were processed during this roster?"

The general steps to develop an ERD are to identify the individual pieces of information required (a case number, a person's name) and the entity types these represent. Document the rules that link them, but only the rules that are meaningful in the context of the problem you're trying to solve. Determine the questions you want the system to answer and ensure it can do so. Reduce the entities to their normal forms. These steps often happen in parallel and cyclically.

In summary, the two diagrams represent two very different sets of business rules and sets of questions that can be answered. Only you can know which better solves your current problem.