Quantitatively, aggregate demand and GDP are the same. They can be calculated using the same formula, and they rise and fall together.
Calculating Aggregate Demand and GDP
In general macroeconomic terms, both GDP and aggregate demand share the same equation:
C = Consumer spending on goods and services
I = Investment spending on business capital goods
G = Government spending on public goods and services
X = Exports
M = Imports
There are three methods for estimating GDP:
Conceptually, all of these measurements are tracking the same thing. Some differences can arise based on data sources, timing and mathematical techniques used.
GDP, AD, and Keynesian Economics
A Keynesian economist might point out that GDP only equals aggregate demand in long-run equilibrium. Short-run aggregate demand measures total output for a single nominal price level (not necessarily equilibrium). In most macroeconomic models, however, the price level is assumed to be equal to "one" for simplicity.
GDP and aggregate demand are often interpreted to mean that the consumption of wealth and not its production drive economic growth. In other words, it disguises the structure and relative efficiency of production underneath total expenditures.
Additionally, GDP does not take into consideration the nature of what, where, and how goods are created. For example, it does not distinguish producing $100,000 worth of toenail clippers versus $100,000 worth of computers. In this way, it's a somewhat unreliable gauge of real wealth or the standard of living.