Elasticity and its types 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).