Java exceptions are categorized into two main types: checked and unchecked exceptions. Checked exceptions, also known as logical exceptions, occur due to anticipated external factors and must be handled at compile time, either by using try-catch blocks or by declaring them with the throws keyword. Examples include FileNotFoundException and ParseException, where the developer is required to address the potential issue by writing specific code to manage it. Unchecked exceptions, or runtime exceptions, arise from programming errors like NullPointerException and IndexOutOfBoundsException and do not require explicit handling, as they occur during the program's execution. The distinction between the two lies in the necessity for checked exceptions to be addressed at compile time, while unchecked exceptions occur at runtime and often result from coding oversights. In the context of microservice architecture, unchecked exceptions can be used to manage situations where a request cannot be fulfilled due to a lack of critical data from a database, allowing the request to be terminated gracefully without propagating unnecessary exceptions through the layers of code.