Cover letter for a PhD application

Dear all,

I am about to submit an application for a PhD position. For the application it is necessary to submit a covering letter and

a CV. I found out, that a covering letter for academic purposes often is called a statement of purpose and has a somewhat different structure compared to a covering letter for non-academic purposes. (But then, on the other hand, the statement of purpose can also be called a covering letter).

I am now a little bit confused. Should I write the covering letter and make it look like a statement of purpose? Or should I write an ordinary covering letter?

And my next question is, how bad is it, in case I choose the wrong kind of covering letter?

I would appreciate some help from those of you who know

Best regards,

Maja