What is the aggregate damand, short & long run relationship?

Short Run vs Long Run AD:
Curve - No different. It is still downward sloping.

Theory - Short Run is the aggregation within a short period of time. It means that the aggregation does not capture long run effect, e.g. population growth. Long Run is aggregation for long period of time. In theory, it captures all possible factors.

Short Run vs Long Run AS:
Curve - Short Run AS is a upward sloping curve, which it is a vertical line for Long Run AS.

Theory - Short Run AS is the aggregation of supply of goods and services for a period of time. Similar to AD, it does not capture any long run effect. Long Run AS is aggregation for a the long run picture. We assume that resources for any goods and services are limited. Also, we assume that the economy is at the full capacity of production in long run. Therefore, Long Run AS is a vertical line on the Max Q of the goods and services.

Illustration (e.g. gasoline)
To produce gasoline, it requires input such as machineries, man-power, and gasoline field certainly. In long run, we assume that all gasoline field is at its full speed of producing gasoline. Therefore, the Long Run AS will be a vertical line at the Max Q of the production of gasoline.

Illustration 2 (e.g. services)
To provide service, it requires man-power. In long run, we assume that there is enough job for all working population, and it implies 100% employment rate. Such that, the Long Run AS will be a vertical line on the total number of population in an economy on Q-axis.

Equiblium
The equiblium will be the intersaction of Long Run AD and Long Run AS.