The demand for toothpaste tends to be inelastic partly because people spend only a very small fraction of the income on toothpaste.  If its price doubles, the income effect are
 
 

There are more substitutes for "pepperoni pizza" (such as sausage pizza, plain cheese pizza, burgers, chicken sandwiches, and so on) than for "food" overall.   So the demand for pepperoni pizza is more elastic than the demand for food.
 

Long-run demand curves show quantities demanded at various prices after people have fully adjusted to a change in underlying conditions.   Short-run demand curves show quantities demanded at various prices before people may have had time to adjust fully to a change.  The same is true for long-run and short-run supply curves.
 
  When a new tax on tobacco products raised the price of cigarettes to $24.00 per pack, Joe cut his smoking from 2 packs to 1 pack per day.  After six weeks, his wife pointed out that he had spent more than $1000 on cigarettes in the past 6 weeks, and threatened to divorce him if he didn't quit.  A few months later, Joe adjusted to the higher price by quitting, and he stopped buying cigarettes.  So his long-run demand for cigarettes was more elastic than his short-run demand.

The following graph starts with an equilibrium at point A, where the supply curve S1 and the short-run demand curve D1 intersect.   A change in some underlying condition causes a decrease in supply from S1 to S2.  In the short run, the economy moves to a new equilibrium at point B, where the new supply curve S2 intersects the original short-run demand curve, D1.         After a while, buyers have time to adjust to the new situation (with a higher price) -- they adjust by (a) finding more substitutes for this good, and (b) buying fewer complements for this good.   As buyers adjust to the new situation, the equilibrium moves from point B to point C, where the long-run demand curve D2 intersects the supply curve S2.  Notice that the price rises by more in the short run than in the long run.