Is there a difference between Luria Broth and Lysogeny Broth? Is there a difference between Luria Bertani and Luria Broth? Or are they both the same thing? Is it necessary to autoclave LB medium after it has been made?

Although both names are quite common, both are wrong. In the original paper from 1951 Bertani was studying the lysogeny in _E.coli_ , hence he called his media for this purpose "Lysogeny Broth" or LB in short. In the subsequent decades this name was transformed to "Luria Bertani" or "Luria Broth", which is incorrect. See the references 1 and 2 for more details.

For the second question: It is absolutely necessary to autoclave the media after preparation to avoid the contamination and growth of microorganisms which are present in our environment. Only making the media sterile makes sure that we can work with defined microorganisms.

References:

1. Studies on Lysogenesis I.
2. The Limitations of LB Medium