Contracts require "meeting of minds"
I disagree with another answer to this question. Specifically, the part that says:
Contracts do not need to have all terms explicitly spelled out for those terms to be binding;
That is incorrect. In fact, contracts have to meet several requirements in order to be valid, binding and enforcable. Most of those requirements are irrelevant to this question... However, one of those requirements is that the parties must have a meeting of the minds as to what they are agreeing. If there is no meeting of the minds on all the terms, then there is no contract. This is a common way contract disputes arise. Lack of clarity of the terms of the contract. And this is how contract disputes land in the legal system.
Contracts are statutory; without one, payment becomes a matter of equity
However, no contract does not mean you don't have to pay. You have to pay as a matter of equity which is a common law principle. The contract would be a statutory basis for owing payment. Without a contract, equity and common law kicks in. Specifically, the principle of unjust enrichment becomes the issue. So a court would have to determine the fair value of the services rendered and you would then owe the fair value.
You could just avoid the potential for a later price dispute by agreeing to the price before hand. But, as the question points out, this is not always done in practice.
Settlement terms revert to the court
That said, if you don't agree on price before hand the other party doesn't just get to charge whatever they want. If they charge more than you are willing to pay, then force them to sue you and a judge will determine what you owe. Both sides will have to present evidence supporting their determination of the value of the services rendered.
But, as mentioned, this can be avoided by either agreeing to the price in advance or an after-the-fact negotiation to arrive at a fair price for settlement.