The phrase "turn into ___" means "become" but is more casual:

I'm becoming a grumpy old man.

There's another difference between "turn into" and "become". You can follow "become" with a noun phrase or an adjective phrase:

It's becoming a huge project.

They're becoming smaller and smaller.

But "turn into" can't be followed by an adjective phrase. It has to be followed by a noun phrase:

It's turning into a huge project.