Couple things:
The test they did is called a block test. When that test is positive, it means there's exhaust particles in your coolant, and it's diagnostic of a blown head gasket.
The reason your truck wasn't starting is because at least one cylinder was full of coolant, due to the blown head gasket. Coolant is a liquid and doesn't compress the way air does, so the starter didn't have the oomph to push your piston through a full cycle. The mechanic fixed it temporarily by pulling the spark plugs and turning the engine over, blowing the coolant out the empty hole, then putting the spark plugs back and starting the truck so you could drive home.
The white smoke when you drove home coming out your exhaust was steam and smoke from the burning coolant.
If you never actually started the truck while the cylinders were full of coolant, you probably didn't bend a rod or do any other damage to the lower end, but you won't know that for sure unless you take the motor apart and look. I suggest you don't try and start it again without pulling the plugs and blowing that coolant out first, and after you do you should top off your coolant and don't drive very far or you'll run out of coolant and overheat and then you WILL need a complete rebuild or new engine for sure.
Replacing a head gasket is not hard, but it is a labor intensive job, and it gets worse if the top of the block or the bottom of the cylinder heads is pitted or out of true, because that means machine work. The mechanic is going to suggest to you that you buy a reman motor and let him put it in, because it's less work for him and less money for you. On the flip side, if you were to do the work yourself, it will cost you MUCH less than replacing the entire motor. Your call.
If you do choose to buy a used motor and have your mechanic install it, I think you should absolutely ask the him about doing things like new plugs and coils, replacing the timing belt/wp, etc. All those things are very easy to do while the motor is out of the truck.
Anyway, you seemed a little lost about some of the terminology, hope I could fill in some of the blanks.