Do some searches on here and you'll find pics of every method.
But a simple answer is texas & carolina rigs refer to weight placement.
Texas rig, is usually a bullet shaped slip weight placed immediately ahead of the hook and bait. it may be left to slide freely or pinned "Pegged" inplace with a small section of toothpic.
Carolina rig, means the weight is positioned about a 1-2ft ahead of the hook & bait.
The weight might be fixed or an oval slip sinker that is held forward w/ a small tiny splitshot.
Split shotting simply means your using a fixed split shot weight. Might be positioned forward carolina style or it may be positioned near the hook Texas style.
Drop Shooting refers to a specific method where the weight is at the end of the line and the hook is tied inline some distance up the line toward the rod.
The sinkers and knots used in drop shotting are rather specific, so read up for further details.
But IMO, drop shotting simply means the weight is at the bottom of the rig.
You may use the actual drop shot weights, or you can use a split shot or two or three, or you may crimp on soem hollow core pencil lead. Which is what I do.
Whacky and inline refer to how you hook the plastic worm on the hook. Inline is just that..inline...through the nose, out the side and back through the worm. Typical plastic worm hooks are used.
Whacky rigged, means you simply put the hook through the worm through the middle. The results in a "whacky" action when bounced up and down. Normally a std octopus style hook is used.
But there are no hard fast rules with any of this.
There are a wide number of variations on all of the above. But generally speaking that is a rough description.
Also "Panfish" refer to fish from the sunfish catagory.....we don't refer to bass as panfish.

There are bass fisherman ..... and then there are panfisherman.
We make a distinction between the two. Even if we fish for both on occasion.

Hope this helps,
Hunt'nFish