aura_component_1.cmp

<aura:component implements="flexipage:availableForAllPageTypes" access="global">
    <div style="padding: 20px;background: white;margin: 10px;border-radius: 4px;height: 120px;">
        <h1 style="font-size: 15px;">Aura Component: Firing Event</h1>

        <c:one_register_event name="testevent" namespace="astro" aura:id="first-event"></c:one_register_event>

        <lightning:button label="Fire Event From Aura" onclick="{!c.fireEvent}"></lightning:button>
    </div>
</aura:component>

aura_component_1Controller.js

({
    fireEvent : function(component, event, helper) {
        component.find("first-event").fire('Fired Event from Aura Component.');
    }
})

aura_component_2.cmp

<aura:component implements="flexipage:availableForAllPageTypes" access="global">
    <aura:attribute name="data" type="String" />
    <div style="padding: 20px;background: white;margin: 10px;border-radius: 4px;height: 120px;height: 120px;">
        <h1 style="font-size: 15px;">Aura Component: Handling Event</h1>

        <c:one_event_handler name="testevent" namespace="astro" onaction="{!c.handleEvent}"></c:one_event_handler>

        <br />

        {!v.data}
    </div>
</aura:component>

aura_component_2Controller.js

({
    handleEvent : function(component, event, helper) {
        component.set("v.data", event.getParam('payload') );
    }
})

demo_component_1.html

<template>
    <div style="padding: 20px;background: white;margin: 10px;border-radius: 4px;height: 120px;">
        <h1 style="font-size: 15px;">LWC Component: Firing Event</h1>

        <c-one_register_event name="testevent" namespace="astro" class="first-event"></c-one_register_event>

        <lightning-button label="Fire Event From LWC" onclick={fireEvent}></lightning-button>
    </div>
</template>

demo_component_1.js

import { LightningElement } from 'lwc';

export default class Demo_component_1 extends LightningElement {

    fireEvent(){
        this.template.querySelector('.first-event').fire('Fired Event from LWC.');
    }
}

demo_component_1.js-meta.xml

<?xml version="1.0" encoding="UTF-8"?>
<LightningComponentBundle xmlns="http://soap.sforce.com/2006/04/metadata" fqn="demo_component_1">
    <apiVersion>45.0</apiVersion>
    <isExposed>true</isExposed>
    <targets>
      <target>lightning__AppPage</target>
      <target>lightning__HomePage</target>
    </targets>
</LightningComponentBundle>

demo_component_2.html

<template>
    <div style="padding: 20px;background: white;margin: 10px;border-radius: 4px;height: 120px;">
        <h1 style="font-size: 15px;">LWC Component: Handling Event</h1>

        <c-one_event_handler name="testevent" namespace="astro" onaction={handleEvent}></c-one_event_handler>

        <br/>
        {data}
    </div>
</template>

demo_component_2.js

import { LightningElement,track } from 'lwc';

export default class Demo_component_2 extends LightningElement {
    @track data;

    handleEvent(event){
        this.data = event.detail.payload;
    }
}

demo_component_2.js-meta.xml

<?xml version="1.0" encoding="UTF-8"?>
<LightningComponentBundle xmlns="http://soap.sforce.com/2006/04/metadata" fqn="demo_component_2">
    <apiVersion>45.0</apiVersion>
    <isExposed>true</isExposed>
    <targets>
      <target>lightning__AppPage</target>
      <target>lightning__HomePage</target>
    </targets>
</LightningComponentBundle>