Listening to music on iphone?

I just got an iphone, its not my first time using or messing with one but it is my first time going into the music. I i bought a couple of songs when i with it when i first got it but when i opened my music, every song i ever bought over the years were there. All the songs have the little download symbol next to them, except for the ones i had just bought using the iphone, when i played the old songs they play all the way. Right now i'm at a place with Wi-Fi, i want to know is the reason all my old songs are on there because i'm connected to the internet or is it always like that?

Your purchases automatically get downloaded

Because you signed in under your old account. Did you connect to your computer? If so, did you sync?

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