Вот Вам примитивнейший пример.
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<script src="http://ajax.googleapis.com/ajax/libs/jquery/3.3.1/jquery.min.js"></script>
<title>Document</title>
</head>
<body>
<div>
<form action="">
<input type="text" name="name">
<input type="text" name="phone">
<input type="hidden" name="first" value="first">
<input type="submit" name="first">
</form>
</div>
<div>
<form action="">
<input type="text" name="name">
<input type="text" name="email">
<input type="hidden" name="second" value="second">
<input type="submit" name="second">
</form>
</div>
<div>
<form action="">
<input type="text" name="name">
<textarea name="textarea"></textarea>
<input type="hidden" name="third" value="third">
<input type="submit" name="third">
</form>
</div>
<script type="text/javascript">
$(document).ready(function(){
$("form").on("submit", function(e){
e.preventDefault()
var data = $(this).serialize()
$.ajax({
url: 'ajax.php',
method: 'POST',
data: data,
success: function(response){
console.log(response)
var answer = jQuery.parseJSON(response);
if(answer.type === 'success'){
alert(answer.text)
}
if(answer.type === 'error'){
alert(answer.text)
}
}
})
})
})
</script>
</body>
</html>
<?php
if(isset($_POST)){
if(isset($_POST['first'])){
if(!empty($_POST['name'])){
$answer = ['type' => 'success', 'text' => 'Отправлена форма First'];
}else{
$answer = ['type' => 'error', 'text' => 'Заполните поле "name" в форме First'];
}
}
if(isset($_POST['second'])){
$answer = ['type' => 'success', 'text' => 'Отправлена форма Second'];
}
if(isset($_POST['third'])){
$answer = ['type' => 'success', 'text' => 'Отправлена форма Third'];
}
echo json_encode($answer);
}
?>
Простой