That is more of a legal question, not an investigation question. But by definition, a contract can be anything agreed to by two parties, verbal, non-verbal (for completing a service, expecting a payment) or written.
Generally running a website, you have to agree to terms and conditions and a privacy policy before the services can be provided to you (ie. upon signing up), so that's a contract.
I think the reason why government websites make you digitally sign a declaration is because of various government laws about making false declarations - eg. tax office making it a criminal offence, thats why you don't see private entities really doing that, but thats just my opinion.
hope that helps.