This is a case of **present perfect simple and present perfect continuous.**

> We use the present perfect continuous to emphasise the duration of an action which started in the past. For finished actions we use the present perfect simple.

>**I've been looking for my dog.** (I still look for him now.)

>**I've looked for my dog.** (I don't necessarily look for my dog any longer.)

>**Present perfect simple or present perfect continuous?**

> We use the present perfect simple, not continuous:
>
 - if the action is finished and complete.

>**I've written a letter.**

 >- if we want to say how often an action has happened.

>**She's broken her leg three times.**

In summary **he buscado a mi perro** y **he estado buscando a mi perro** don't mean the same.