Is jailbreaking and unlocking an iPhone the same thing?

I have a iPhone 3G and I want to connect it to simple mobile but it has to be unlocked first

No it's not. Jailbreaking is just something you do to to your Apple device which allows you to do things to it that Apple didn't allow before. I believe it usually come with an app called Cydia.
When you buy a phone, it's usually locked to a certain phone contract company, unlocking it means that you can use that phone with another company than the one it was on by default. I believe you can pay certain phone providers to unlock it for you.

No jailbreak is so you can get all the apps for free and an unlock is so can put it with any carrier like Verizon wireless, AT&T, sprint, t-mobile, etc.

No, one is changing the software on your iPhone to a hacked version of the iOS, the other is unlocked from the carrier side (in a database). Carrier unlocks are permanent and updates will not affect them, jailbreak unlocks could be affected by updates. Jailbreaking can also render your phone inoperable if not done correctly.

NO. Jailbreaking can cause permanent damage to your phone and may be slow. On the other hand, Unlocking works best and won't cause any damage and if you decide that you don't want it anymore you'll get a lot more money if its unlock.
**I wouldn't recommend jailbreaking. Just throwing that out there.

Jailbreaking is done to use any 3rd party apps, music, software which all Apple didn't allow before. Jailbreaking is done using software/firmware.
While unlocking is making your iPhone to work on any GSM network. IPhone can be network unlocked from http://www.unlock-zone.com/apple-iphone-4/rs5wp9/ by providing the country and network to which the phone is locked. IPhone can be remotely unlocked here.