To find out which button was clicked in a component containing multiple buttons, we can use Component.getLocalId().

Here is an example with multiple lightning:button components. Each button has a unique local ID, set by an aura:id attribute.

Sample Lightning Component:

<!--Sample.cmp-->
<aura:component>
    <aura:attribute name="clickedButton" type="String" />
    <div class="slds-m-around_xx-large">
        <p><b>You Clicked: {!v.clickedButton}</b></p>
        <br/>
        <lightning:button aura:id="button1" name="btn1" label="Click Me" onclick="{!c.buttonClick}"/>
        <lightning:button aura:id="button2" name="btn2" label="Click Me" onclick="{!c.buttonClick}"/>
    </div>
</aura:component>

In the JS controller, we can use one of the following methods to find out which button was clicked.
event.getSource().getLocalId() returns the aura:id of the clicked button.
event.getSource().get("v.name") returns the name of the clicked button.

Sample Lightning Component JS Controller:

({
    buttonClick : function(cmp, event, helper) {
        var clickedBtn = event.getSource().getLocalId();
        alert(clickedBtn);
        cmp.set("v.clickedButton", clickedBtn);
    }
})

Lightning Test App:

<!--Test.app-->
<aura:application extends="force:slds">
    <c:Sample />
</aura:application>

Output: