A contract is simply a mutual agreement.
Which reminds me, is it even legal to use contracts that weren't made by lawyers? I mean, being legal binding and such, I'd think it's something that should only be handed to the relevant professionals.
On a related note, what would artists say if there was a clause allowing for the client to ask more assets without need to filling out a full new contract? Assuming such a clause makes it explicitly clear under which conditions this would be, including the amount of extra payment, the amount of time that must be allowed to do the job, etc. (and assuming those conditions are designed to match the ones from the original assets)
If a homeowner agrees asks a neighbor kid to mow his lawn that becomes a binding verbal contract. Courts rule on verbal contracts all the time and routinely find that they are binding.
An email chain where both parties agree to something can also be considered a binding written contract.
As Washu points out in his rather long reply, when a lawyer writes a contract they use specific language with specific meaning. When a non-lawyer has an email chain discussing what must be done, what must not be done, how payment is to be made, etc., then plain language is used and the judge must interpret it.
The written agreement in plain language is still binding.
Attempting to write your agreement in 'legalese' is a very risky thing to do; you are using language with a specific meaning that might not mean what you think it means. Accidentally omitting or over-specifying details can void your agreement. That is generally not the case with a plain language agreement.