Iphone 3gs jailbreaking and unlocked

Okay so yes I'm new to the iphone stuff, but I was looking up stuff and basically everything said you can jailbreak but not unlock, but you can't unlock unless you jailbreak. And I bought a 3gs on ebay that was unlocked so I thought it would be jailbroken. I just got the fone and my tmobile sim card works so obviously its unlocked, but when I looked for apps that I heard about for jailbroken fones I don't see any. Is there something i'm missing? And If I need to jailbreak it, will it get messed up that its an unlocked fone? Thanks!

Added (1). I thought it would already be jailbroken, being unlocked I thought it needed to be jailbroken first. But I don't see anything in the phone. Any recommended websites that have guaranteed ways to jailbreak?

Jailbreak and unlock are both different thing. You can both unlock and jailbreak your phone. You need to jailbreak your phone for you to be able to download third party apps and themes. And jailbreak won't mess with your unlock.

Your 3GS looks like it's originally unlocked! And unlocking might not need jailbreaking as you are saying: IMEI unlocks or sim interposers are a perfect example of this.
The jailbreaking process will NOT do anything to your unlock, you can use it tho to install as the other person said 3rd party apps and themes.
Though if you are willing to do that, avoid installing pirated/cracked apps, as these could damage your phone.

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