"Pre-Qualification" is a much abused term. There are really two ways to obtain infomation from a lender showing if you have the ability to qualify for a loan. In each case below, the lender must send you a Good Faith Estimate, Truth-in-Lending statement, appropriate state disclosures, and a letter specifying the terms under which the lender expects to provide you with financing.
"Pre-Qualification" means that a loan originator has taken information from you verbally about your income, assets, and employment. A credit report is ordered as well. Based on your verbal answers, the loan originator gives you a rough idea of the loan amount you might obtain, possible rate of interest, and likely down payment. Often, the information is input to automated loan approval software (such as Fannie Mae Desktop Underwriter, Freddie Mac Loan Prospector, of FHA Total Scorecard) to provide a quick analysis of your ability to qualify. Pre-Qualifications are issued by loan origiantors or sometimes automatically by a lender's retail web site.
"Pre-Approval" means the lender's underwriter has been given copies of your paychecks, copies of your most recent bank statements, verified employment, verified rent/prior mortgage history, copies of your W-2s and/or tax returns... basically everything needed to underwrite and approve your loan except for the executed purchase contract, appraisal, and title commitment. A Pre-Approval is issued by the underwriter. Techinically, it is an Approval pending certain conditions to be cleared.
"Pre-Qualifications" are very fast (usually taking 10-30 minutes) and are useful for comparing lenders, but since they rely on verbal inforamtion from the borrower, they are highly inaccurate and basically worthless for pursposes of making an offer (not necessarily the borrower's fault - there is a lot of detail in underwriting income, assets, credit, and employment).
If you provided information over the phone, you have a "Pre-Qualification". Your Realtor needs some evidence that you will be able to obtain financing to complete the transaction (unless you're paying cash, of course).
"Pre-Approvals" are much more reliable since (1) An underwriter has completed a preliminary credit decision and (2) all of the qualifying on the buyer's side of the transaction is complete. No one but an underwriter may make any commitment to lend on behafl of a lender.
Since you are ready to make on offer, it would be very wise to submit a full application for a Pre-Approval decision to the lender's underwriter as soon as possible. You're going to have to do it anyway (so why not start now), and if there is a discrepancy between the loan originator's estimate and the underwriter's decision, you'll want to know as quickly as possible to take appropriate corrective measures.