What is the difference between LC and LG, and Why we need both of them and in which situation..?

Letter of credit: it is a document issued by the bank when one party buys certain goods and needs to ship it, therefore guarantees the second party that costs will be paid if the terms and conditions are fulfilled.

Letter of guarantee: is issued by the bank at the request of one party in order to use it when conducting a deal or entering a bid

These are two types of financial facilities (services) offered by banks to facilitate and moderate commercial transactions between parties who (1) do not know each other very well (2) do not trust each other very much and/or (3) in case things go wrong for some unknown/unforeseen reasons

Letter of credit (LC) is usually used in international trade across borders when the buyer and the supplier are in two different countries and fall below two different financial/legal systems.  LC ensures timely payment to the supplier upon fulfiining the conditions/criteria for the payment. 

Letter of Guarantee (LG) is somehow different because it applies between the buyer and the supplier even if they are in the same country as long as the other conditions mentioned for LC may still apply.  LG in this case insures the supplier will be paid in case the buyer defaults on on payment or if there is any dispute between the buyer and the supplier that cannot be resolved directly.