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For commercial banks and large finance companies, "loan agreements" are usually not categorized although "loan portfolios" are often broadly characterized into "personal" and "commercial" loans while the "commercial" category is then subdivided into "industrial" and "commercial real estate" loans. "Industrial" loans are those that depend on the cashflow and creditworthiness of the company and the widgets or service that it sells. "Commercial real estate" loans are those that repay loans but that depend on the rental revenues paid by tenants who lease space, usually for extended times. More granular categorizations of loan portfolios exist but these are always variations around the larger themes.
The first thing that should be checked while signing the agreement is the interest rate as it may create stress on you while repaying the loan amount. With the current income level, you should be able to validate whether you can afford to repay the loan at the interest mentioned in the loan agreement.
There are many financial institutions that offer private student loans with bad credit. The only fuss in the deal is the requirements of the financial institutions. Most entities that I know of providing this service would require a Co-borrower or a Co-Signer. This means as a student you and your parents would need to sign on the loan agreement agreeing to repay the loan.
Prior to entering into a loan agreement, the "borrower" first makes representations about his affairs surrounding his character, creditworthiness, cashflow, and any collateral that he may have available to pledge as security for a loan. These representations are taken into consideration and the lender then determines under what conditions (terms), if any, they are prepared to advance money.