What’s your credit score? Depends on what you’re buying.

Erik Anders Nilsson, of the Jersey City Peace Movement, looks through his wallet prior to the start of a rally led by the “Occupy Wall Street” movement, in front of the Goldman Sachs building, Thursday, Oct. 6, 2011, in Jersey City, N.J. The protest comes a day after colleges staged walkouts and hundreds of people marched in lower Manhattan. (AP Photo/Julio Cortez)

Consumers often misunderstand something rather basic about credit scores: They think that each person has only one, when in fact a person has dozens of them under the nation’s most widely used credit scoring formula, known as FICO.

For starters, there’s a base score, which is commonly used by mortgage lenders. There are customized scores for specific types of lenders, such as those that issue credit cards or auto loans. And the software that cranks out these scores is often updated, so different lenders may be using different versions with different results. In other words, when you pull your credit score, you may not be looking at the same three digits as your bank.

The Fair Isaac Corp., developer of the FICO, said it wants to demystify the numbers. On Monday, the San Jose-based firm announced that consumers who pay to pull their base scores from the company’s Website – www.myfico.com – also will get the customized scores used for auto loans and credit cards at no additional cost.

“Depending on how you count it, there could be up to 50 different FICO scores for a single consumer,” said Jim Wehmann, an executive vice president at the company. “We will show the most widely used 18, and that covers 92 percent of the FICO score versions used by the nation’s lenders.”

Making sense of those 18 requires understanding how credit scoring works.

The nation’s three largest credit reporting agencies — Equifax, TransUnion and Experian — use FICO software to calculate credit scores. They then sell the scores to lenders. (Those scores range from 300 to 850. The higher the number, the stronger the rating.) Here’s how the base score is weighted for the general population:

The relative importance of the above categories varies if a lender decides to use a specialized score to determine someone’s creditworthiness. For instance, the FICO auto score pays special attention to a consumer’s payment history on car loans whereas the scoring formula for bank cards puts more emphasis on how much credit is available to a consumer, and how much of it they’ve used as well as the history of their credit card accounts. These considerations could lead to a difference between a person’s base score and the various specialized scores.

“Those differences could be very close, but they can also be wide,” Wehmann said. “The only way for people to know is to show them the numbers.”

Even when the differences are small, the fall-out can be big.  “A 20 point difference on your credit score can be the difference between an approval or a denial on a loan,  or the difference between the best interest rate or the second best interest rate,”  said John Ulzheimer, president of consumer education at CreditSesame.com, a credit management Website.

Here’s more from Ulzheimer on why a credit score matters.

The myfico site also offers simulators that project how various scenarios can affect your score, such as paying down a credit card or filing for bankruptcy. There are also tools that can analyze your score based on areas of strength and weakness.

As for the price of pulling your FICO credit scores, it varies.

The cheapest — at $19.95 — involves pulling one credit report and one generic credit score from one credit agency. Under the plan announced Monday, the customized scores for auto and credit cards from that credit agency would be included for free. If you buy credit reports and generic scores from the other two agencies, you pay more, and you get their customized scores at no additional cost.

It’s unlikely that each credit agency would give the same score to the same person because the agencies collect their information from different creditors. Even when they collect from the same creditors, they update their records at different times.

That’s why mortgage lenders generally pull FICO scores from all three bureaus, said Ulzheimer of CreditSesame.com.They then base their lending decisions on the middle one of the three scores.  If a couple is applying jointly, then six credit reports and six credit scores are pulled to get the most accurate picture possible.

Fair Isaac officials said that consumers who tap into myfico.com will only get the customized scores provided by Experian and Equifax for now. The company expects to have the Transunion scores available within a few weeks.

More than a year ago, the company announced that any lender using any version of the FICO score can share the score they use to manage a customer’s account with the customer for free. Many credit card issuers jumped on board, and FICO estimates that more than 60 million consumers now have access to their credit scores through this program.

Keep in mind that by law the three credit bureaus are required to provide consumers with free copies of their credit reports once every 12 months through AnnualCreditReport.com. But as my colleague Michelle Singletary recently reported, people are not entitled to free credit scores, which have become a big business. While many companies promise access to a free score, the deal can often come with a catch – a trial credit-monitoring service. Forget to cancel, warned Singletary, and you’re billed a monthly fee.