A "living" trust only means that the trust came into effect when the person who set the trust up was alive (vs. a "testamentary" trust which comes into effect after the person setting it up has died - that is, it's a trust created in a person's last will and testament).
So either a revocable trust or an irrevocable trust can be a "living" trust.
A revocable trust gives the person who made it the right to make changes in the trust - who gets what and when they get it. If assets are held in a revocable trust, they are not protected against creditors' claims and are counted as part of the "grantor's" estate when the grantor dies.
An irrevocable trust cannot be changed (technically, there are ways to change it, but usually you have to seek court permission to do so) - who gets what and when they get it is determined at the time the trust is set up and you can't change your mind later.
In some states you can set an irrevocable trust up for yourself and have the assets in it be protected against your creditors (California is not one of those states).
Most of the time irrevocable "living" trusts are used to make gifts to children, grandchildren, or others. Many times they are "funded" with insurance policies - the person who is named as the trust manager (the "trustee") pays the insurance premiums with money that the person who set the trust up (the "grantor") contributes to a trust bank account. Then, when the insurance pays off (usually at the grantor's death), the entire amount of the insurance policy is outside of the grantor's estate for estate tax purposes.
Irrevocable trusts do not need to be used only for insurance - you can contribute cash, stock, real estate, or other assets to them. Depending on how the trust is set up and the value of what you're contributing, you might need to file a gift tax return or even pay gift taxes on the value of the contribution.
As to why you would choose one type of trust vs. another - the answer depends upon what you're trying to accomplish and when you want to accomplish it.
The information you obtain at this site is not, nor is it intended to be, legal advice. You should consult an attorney for individual advice regarding your own situation.
I agree with Attorney Brewer. A Living trust is typically a revocable trust and this just means that you are able to change it throughout your life. It does not offer any credit protection. The assets in the revocable trust are subject to estate tax (exemption is currently $5,000,000).
An irrevocable trust offers the ability to avoid estate tax (such as an irrevocable insurance trust) at the time of your death. Technically, you have given the asset to the trustee of the trust (which can't be you) and therefore, you have no direct control over the asset.
Sometimes an irrevocable trust is created for asset protection such an off shore trust; however, these are not typically done for the average client.
There are other irrevocable trust for charity, such as a CRT that allow for an income tax deduction for your income taxes and provide your charity of choice a donation.
Most people just set up a revocable living trust.
No attorney client relationship is created by this offer of general advice. It is very important to have a consultation with an attorney to know your specific rights in any given case.
One more additon to the answers above, it is generally better to establish a living trust during your lifetime rather than a testamentary trust (one that will be created after your death via your Will) because the living trust will avoid Probate as long as all of the assets have been properly titled/funded into the trust.
This does not constitute legal advice nor does it create an attorney-client relationship.