When I bought my acoustic guitar, it had electric guitar strings on it. (or rather generic strings that can go on either).
I’ve look in the guitarstore, and they sell strings that cost $40 for 6 strings, but are made purely for the acoustic.
Will these sounds better?

New strings are the best way to get a guitar to sound better. You don’t need to pay $40 for a set. There are several good brands which cost about half that for a set (D’Addario, Elixir, Martin). Start with light guage strings. Mediums sound better on some guitars, but but some guitars can’t handle the tension. Lights will be easier on your fiingers, too.
Electric guitar strings are way too light.
You will be amazed at your new sound when you get proper acoustic strings.

It takes a day or so for the strings to stretch out and reach an equilibrium, so you may have to tune up frequently at first.