What is the difference between inheriting property and receiving property as a gift?

Inheritance Tax:
Current income tax law provides for a "step-up" in the basis of an inherited asset to its fair market value at the time of the decedent's death. When the heir sells the asset, the capital gain for income tax purposes is measured by the difference between the heir's selling price and the stepped-up basis of the asset. (The basis is no longer the asset's cost at the time when the decedent acquired it. That would be known as a "carryover" basis.) As a result, there is no income tax liability on the appreciation in the asset's value during the decedent's period of ownership (lifetime) -for the decedent as well as the heir. [http://www.policyarchive.org/handle/10207/1162]
Gifted Property:
If you give real estate to your children while you are living and then live at least one year, your children do not pay inheritance tax on the property received. However, your children would receive “carryover” basis in the asset. “Carryover” basis is the value you paid for the property. For example, if you purchased property for $10,000 then you would have a $10,000 cost basis in the property. When you give the asset to your children, they receive your basis in the property or “carryover” basis in the real estate. When your children sell the asset, they recognize capital gains on the difference between the fair market value (selling price) and the “carryover” basis. Therefore, your children will be paying more in income tax.