iPhones are pretty decent, in terms of the quality of recording, but they are kind of blunt tools. Firstly, they take loud sounds and make them quieter and they take quiet bits and make them louder. That's what a phone needs to do - cope with people speaking at arms length, or trying to talk in a Metallica Gig. One microphone is also difficult to place properly to get the right sound between wanted and unwanted stuff. You mention you want to record songs - so you singing, and what? A piano in the room, a guitar, or a karaoke style backing track? All these things mean a phone is just one bit. You need to take the voice and blend it with something else. For a piano - you could put the phone (or single mic) in the right place and hit record. However, with a backing track, how will you hear it? A phone won't let you play back the track into headphones and record your voice at the same time. Computers with audio interfaces and a real mic can.
Only this week I got asked if I'd be willing to play stand by me for a wedding (by a stranger who had heard this on YouTube, and he sent me links). I asked if he wanted somebody to do the accompaniment, or was he wanting a little PA system and a backing track? Confusion - what for, he said? He'd not noticed that the song had loads of other important content apart from the tune - and that doesn't start at the beginning! Use this as an example - a phone would be really the wrong tool. An Sm58, a cheap audio interface and software on the computer is the way to go. Then, you can add a second mic for the piano or other instrument - or use a track, it doesn't matter.
If this makes sense - ask a few more questions and we can take you through it.