how do I buy albums on Apple Music

Music can be purchased on iTunes Store. After the purchase you own the music.

Apple Music (the subscription service) gives you the right to listen to the whole Apple Music catalogue (in streaming or off-line) as long as the subscription is active. The music, in this case, is "rented".

Hi,

I will also add that if you have previously downloaded the tracks from Apple Music, make sure that you delete them before purchasing from iTunes Store.

Jim