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Java applets and standalone applications serve similar purposes but function in fundamentally different environments. Standalone applications are self-contained programs with a main method acting as the entry point, necessary for the Java Virtual Machine (JVM) to start execution. Unlike applets, standalone applications do not rely on a web browser and can run with the Java runtime directly.

Applets, on the other hand, are Java programs designed to be embedded within a web page and run in the context of a web browser or an applet viewer. The browser provides the necessary interface and lifecycle management, eliminating the need for a main method. This distinction facilitates different use cases, where applets are ideal for interactive web content, while standalone applications are suited for more comprehensive software tasks.

The init method plays a critical role in the lifecycle of a Java applet. It is akin to the setup phase of an applet, where initial parameters are configured, and resources are loaded. Executed only once, this method is the first to be called when the applet is loaded by the browser or applet viewer.

Think of init as the construction phase of a building — it's where the foundation is laid. For developers, this method is the spot to initialize variables, set up the user interface components, or load any required resources such as images or configuration files. By handling these initial setups, init prepares the applet to smoothly run and interact with users without delay or additional resource loading during the execution.

After the init phase, the start method takes the stage. Called immediately after init, when the applet is made visible on the web page, start signifies the applet's readiness for interaction. Additionally, this method is called each time the user returns to the page containing the applet, which may not be just once in an applet’s lifecycle.

In essence, the start method breathes life into the applet, allowing it to begin or resume actions, such as animations or audio playback. It’s crucial for activities that should not run continuously in the background, conserving resources when the applet isn't visible. Developers use the start method to kick-off threads or timers that power the dynamic aspects of the applet.

Completing an applet's lifecycle are the stop and destroy methods. The stop method is called by the web browser or applet viewer when the applet is about to be hidden or when the user navigates away from the page. It is the perfect place to pause animations or other heavy-processing activities, effectively putting the applet into a standby mode.

The destroy method is invoked when the applet's life is conclusively over — when the page is closed, or the browser is shut down. This method is responsible for the final cleanup, releasing resources such as memory, threads, or system resources that were in use. It's analogous to a check-out process, ensuring that everything the applet used is properly disposed of to prevent any leaks or lingering processes.