What php code do I use to know if data is being received from a given form?

A simple way to do this, only with php / html is to define a hidden one that identifies which form to trigger, in this example I imagine that both use the same action. You can also do this with javascript.

Example - simple.

<form method="post" action="">
    <input type="hidden" name="tipo" value="pf">
    CPF: <input type="text" name="cpf" value="111.111.111.11" />
    <input type="submit" />
</form>

<form method="post" action="">
<input type="hidden" name="tipo" value="pj">
    CNPJ: <input type="text" name="cnpj" value="222.222.222.222/22" />
    <input type="submit" />
</form>

<?php

if($_POST['tipo'] == 'pf'){
    echo $_POST['tipo'] .'-'.  $_POST['cpf'];
}else if($_POST['tipo'] == 'pj'){
    echo $_POST['tipo'] .'-'. $_POST['cnpj'];
}

In addition to the appropriate solution posted by @rray, you can use the submit fields to differentiate the forms:

<form method="post" action="">
    CPF: <input type="text" name="cpf" value="111.111.111.11" />
    <input name="enviar_pf" type="submit" value="Enviar"/>
</form>

<form method="post" action="">
    CNPJ: <input type="text" name="cnpj" value="222.222.222.222/22" />
    <input name="enviar_pj" type="submit" value="Enviar"/>
</form>

<?php
  if( isset( $_POST['enviar_pf'] ) ){
     echo 'CPF: '.  $_POST['cpf'];
  } elseif( isset( $_POST['enviar_pj'] ) ) {
     echo 'CNPJ: '. $_POST['cnpj'];
  }

Note that in the case you posted, you would not even need this because, as there are fields of the name, you can test them directly: isset( $_POST['cpf'] )

An alternative that works perfectly even though it is not exactly within specs , is to add a GET parameter in POST:

<form method="post" action="?tipo=cpf">
    CPF: <input type="text" name="cpf" value="111.111.111.11" />
    <input name="enviar_pf" type="submit" value="Enviar"/>
</form>

<form method="post" action="?tipo=cnpj">
    CNPJ: <input type="text" name="cnpj" value="222.222.222.222/22" />
    <input name="enviar_pj" type="submit" value="Enviar"/>
</form>

<?php
  if( $_GET['tipo'] == 'cpf' ){
     echo 'CPF: '.  $_POST['cpf'];
  } elseif( $_GET['tipo'] == 'cnpj' ) {
     echo 'CNPJ: '. $_POST['cnpj'];
  }

In this case, notice the action passing the "type" by query string ?tipo=