A Letter of credit (LC) in simple terms, is a guarantee given by the buyer's bank to the supplier or his bank situated in the same country or a foreign country. Usually LC limit is part of one's CC limit. For eg. if you have a CC limit of 10 lakhs with your bank that may include LC limit of say 2 lakhs. Your bank will issue LC for maximum of 2 lakhs. It is nothing but a overdraft facility extended by the bank.
Whereas Bank guarantee (BG) involves actaul deposit of money or given on the basis of a FD. BG can be understood as a deposit, but the guarantee of which is taken by the bank after considering deposited monetary security by you. BG is generally given for tender purposes or any govt benefits as a security deposit.