There are many differences between a claim and a cash bid, but to put it simply-
An insurance claim estimate is an estimate that is figured, using industry-standard estimating software, when your home has sustained damage that is covered by your insurance policy. Insurance claim estimates are initiated when you make a claim. The adjuster comes out to assess the damage and the process begins. You are free to choose who you want to use to do the work. But regardless of who you choose, you must still pay your deductible. It is the law. Your deductible is the same as a co-pay in your health insurance. You pay your doctor the co-pay and pay the contractor the deductible.
A cash bid is an estimate you seek when there is no insurance claim involved in the restoration. You are liable to pay the total amount of the bill on a cash bid. This is usually the way homeowners choose when the property has just been worn from years of use, but not from damage.