Internal storage, phone storage and SD card
Yes.  There's also several other partitions in the internal storage, which is what the other 1GB is taken up by.


/boot - Contains the bootloader, ramdisk image, and the Linux kernel image.

/system - Contains all the OS stuff (Both Linux and Android) as well as built in system apps (e.g. the launcher and the dialer).

/recovery - Contains the recovery OS, which is used for updating as also recovering from situations that prevent booting into Android proper.

/data - This is what you see as "internal storage".  This is where all your user installed apps (both from the play store and any other sources) go, as well as where they save their data.

/cache - Exactly what it sounds like.  Various bits of frequently needed stuff stored in a quick to access manner.

/misc - stores various miscellaneous system settings.

1.5 "Phone storage" is basically like a built-in SD card as far as the OS is concerned.  It's general user storage.


What exactly are you trying to install?  The internal storage (/data above) is where an app generally goes, but particularly big apps (e.g. games like the Asphalt series) will store the large resources in a user partition by default (rather than optionally via the "move to SD" option).