IPhone VS iPod

Question

Almost two years ago I bought me an iPod Touch to listen to my music.  I only bought a 4GB because I didn't really see myself buying 4GB worth of music.  But throughout its use I started to realize the iPod isn't just a music player; I was able to use Safari, get on Facebook, use Twitter and Youtube, and play dozens of apps off the app store.  In other words, it's pretty nifty.
Well like I said, it's been almost 2 years.  The battery is going bad and dies within 20 minutes of use.  I've been planning on getting me a new iPod, but then I started to compare it to my cousin's iPhone.
Now I ain't exactly tech-savvy, but as far as I can tell the iPod and iPhone are one in the same.  The iPhone surely has a bigger battery, better operating system, and can call/text/etc, but as far as general features and use goes they're pretty much the same.  So I started to wonder "Why not just buy an iPhone instead?"
I was wondering if I could just buy me an iPhone and use it like an iPod.  No, I don't want to hook up to no cellular plan, and I ain't gonna be using it to text or call folks.  I'm just gonna charge it overnight, listen to my music, use Safari (I got WiFi at my house), and play my games and use my apps.  I'm just gonna use it like I use my iPod.  I figure the iPhone has better updates though, and not to mention better battery life, and it can run a lot more apps than my iPod ever could.  Plus, if I ever want a phone, I'll already have one.
So is this possible?

Answer 1

No, not with a new iPhone.
None of the functions work with a new iPhone until it is activated, and you will pay much more at the full retail sales price for an iPhone than with a new iPod Touch.
I am going to use MobileKarma.com to get me an iPhone (or iPod), so money ain't no problem.  As for activation.... are you saying my iPhone won't do anything until it has a service on it?
The current iPod Touch runs the same iOS version as the current iPhone models.
The battery is not much different between the current iPod Touch model and iPhone 5S.
http://www.apple.com/ipod-touch/specs.html
Music playback time: Up to 40 hours when fully charged
Video playback time: Up to 8 hours when fully charged
https://www.apple.com/iphone-5s/specs/
Video playback: Up to 10 hours
Audio playback: Up to 40 hours
There are games which will only run on an iPhone.  And some games/apps run smoother on the iPhone.  That's what I meant by 'operating system'.
And thanks for the info on the battery.