A line of credit is somewhat like a personal credit card: The lender disburses funds as they are requested, up to a preset limit. The borrower pays interest (and usually a portion of the outstanding balance) on the amount of funds outstanding at the end of each borrowing period, usually monthly.
An installment loan gives the borrower a lump sum of money and sets a schedule for regular payments over a set period of time for repayment.
A short-term loan is money advanced for a specific purpose: to pay for inventory, to help a company get past a cash flow problem related to accounts receivable, and so on. The loan is expected to be repaid once the immediate need has been resolved.
A long-term loan is aimed at capital spending, including equipment and real estate, and is intended to be repaid from the ongoing proceeds of the company.