What is the difference between a Last Will and Testament and a Living Will?

These are two very different documents, even though they have similar sounding names.
A Last Will and Testament (commonly referred to as simply your "Will") comes into effect the moment you die. It does absolutely nothing all the time you are alive, and can be updated throughout your life. Your Last Will and Testament has a few very important elements. Firstly, it allows you to appoint an estate administrator, also called an "estate trustee" or your "Executor".
The Last Will and Testament also allows you to name a guardian for your minor children in case both parents are no longer available to look after them. Your Will is the only place in which you can name a guardian for your children.
Finally, the Last Will and Testament allows you to describe the distribution of your estate. In other words, who will receive what. This includes your real estate holdings, bank account and possessions. As well as any other financial assets that do not already have a named beneficiary on the asset. Your Will allows you to leave your house to your children, right through to a teapot to your niece. It also allows you to make charitable bequests (a "bequest" is something that you leave to somebody - the beneficiary, in your Will). Bequests can be sums of money, objects or even a percentage of your entire estate.
A Living Will is completely different. It is only in effect while you are alive, but you have lost capacity. It ceases to function after you have died. A Living Will is usually made up of two separate documents. The first is your "Advance Directive" that allows you to express the types of life sustaining treatments you wish to receive; whether you want to be kept alive by machines for as long as possible, or whether you want a "do not resuscitate" order. Together with this Advance Directive, is the naming of a Healthcare Representative, or "Healthcare Proxy". This is the person that you entrust to make healthcare decisions on your behalf if you are no longer able to speak for yourself.
The Last Will and Testament and Living Will sound similar, but are very different documents.