Does 'infinitely elastic' and 'inelastic' pertain to same meaning? What is the difference between them? Please explain in brief.
No. In fact, they mean quite the opposite. Infinitely elastic, means the elasticity is infinity. Perfectly Inelastic means not elastic, i.e. the elasticity is 0. Ineslastic means the elasticity is very low, so between 0 and 1. This means there is "underreaction" (less than proportional).
So if something is infinitely elastic there will be an extremely large reaction. If something is perfectly inelastic there will be no reaction. If something is inelastic, there will be very little reaction.
Let's take the example of price elasticity for an ordinary good where price increases cause demand to fall.
A good with a very close substitute would have a large price elasticity. If it's infinite: At a given price there will be a given demand. As soon as we increase the price even marginally the demand will fall to 0.
A good with no substitute and especially addictive goods usually have a price elasticity of (close to) 0 typically. There is the same demand at all prices. Assume an individual who always must smoke a pack of cigarettes a day. If we increase the price of cigarettes and if his elasticity is 0, then he will continue to purchase one pack a day. Even if we double the price or more, there will be no reaction (in this case reduction).
Elasticity is a general concept which basically means how sensitive one quantity is with respect to some other quantity. In economics we use concepts like price elasticity of demand, elasticity of substitution etc. A high value of elasticity say for example price elasticity of demand means that the quantity demanded is too much sensitive to the price. This will be represented by a horizontal curve between price and quantity demanded and the demand is said to be infinitely or perfectly elastic. A very low value of price elasticity of demand means that the demand is not much influenced by the price. In such case the demand is said to be perfectly inelastic. Price elasticity is majorly governed by consumer needs and availability of substitutes. Although it is difficult to find perfectly elastic or perfectly inelastic goods around us but still we can understand highly elastic goods with the example of, say, a book on economics in printed form. If its price increases even by a small amount people have many substitutes such as online free books or books by other authors. Its demand may fall drastically. An inelastic good could be the air we breathe, water we drink etc. Even if you are charged heavily for it you may not reduce your consumption. But one point to be noted here is that it depends on the consumer utility which goods can be regarded as elastic or inelastic and it may vary from consumer to consumer. For example, oil can be an inelastic good for a millionaire but not for someone poor who can barely afford a rise in oil price.