Both Event Handlers and Event Listeners in JavaScript are used to manage and respond to events triggered by user interactions and other occurrences in the web pages. These are crucial for user interactions and help developers create dynamic and responsive web pages.

Event Handlers:

Event Handlers are the functions that are directly linked to the HTML elements. These are responsible for handling specific events such as clicks, mouse movements, key presses, form submissions, etc. These functions are executed when associated event occurs.

Example of an Event Handler-

<button onclick="myFun()" id="btn">click here</button>

const myFun = () =>{
    console.log("button clicked");
}

In the above example `onclick` attribute is an event Handler that specifies `myFun()` to be executed when the button is clicked.

Event Listeners:

Event Listeners are more flexible for handling events in JavaScript. These can be attached to HTML elements enabling the code to listen for the events and respond to them. This method allows great control over events and performs multiple event handling for a single element based on events triggered.

<button id="btn">click here</button>

const myButton = document.getElementById('btn');

function handleClick() {
  console.log('Button clicked!');
}

myButton.addEventListener('click', handleClick);

In the above example, an event listener is attached to a button element using its id `btn` and when the button is clicked the `handleClick` function is called.

Key Differences:

1. Inline vs. Unobtrusive: Event handlers are typically implemented directly from the HTML tags making the code less maintainable and harder to manage, whereas Event Listeners are maintained in separate JavaScript files promoting a more organized and manageable codebase.

2. Multiple Events: Event Listeners allow many functions to be attached to a single event providing the flexibility of performing multiple actions for a single event.

3. Dynamism: Event listeners are more dynamic and can be added or removed during runtime, enabling developers to create more flexible and interactive applications.

In summary, event handlers and event listeners both serve the same purpose of handling events in JavaScript, but event listeners offer more flexibility, better separation of concerns, and enhanced control over event handling in comparison to event handlers. They are the preferred method for managing events in modern web development.