Minecraft – Is it possible to run 2 different minecraft worlds with 1 modpack in each

Yes, this is doable, but you will need, as ratchet freak pointed out, a separate copy of minecraft for each set of mods. multiMC is one way to do that, but if you upgrade to the new launcher, you can create custom profiles, each with a separate set of mods, to make it even easier (see here for details, since the new launcher adds a couple of steps to the modding process).

Also, once the new launcher is more mature, and Mojang finally get around to providing official mod support, the whole process of switching mods on and off will probably get even easier.

If you are just wanting to add a few mods then you can do this to tekkit lite. Go to %APPDATA%/roaming/.technic/modpacks/"name of pack here" and place the mods in the mods folder. If you do this, then be sure to make a copy of the modpacks's folder as it can be reset from time to time.

Other than that, you can use multi mc which allows you to have many different profiles as well as easily install forge and other mods.