Well, the "contract" is your specific written requirement to another person to the work.
Now, if you are "buying" goods or services from another company, then - well, yes, it is a formal contract we are used to seeing complete with bid specifications and warranties, and "lawyer-talk" about money, etc. But a 'contract": is also a simple drawing or requirement for a welder and supplier in the back office to buy and install a resistor or a motor, weld up a fabricated support for the motor, and hookup a battery strong enough so the rocket motor vibrations won't break both the motor and battery.
What does help while writing the contract/drawing/specification/purchase order is a formal ANSI or NASA or MIL-SPEC because those have been tested and people are used to seeing them. They might be more rigorous than what you need, thus more expensive. But they are also "expected" and so can be delivered at the higher price. A local specification from a local single company might be more expensive, and you are making assumptions - as you wrote above - about the trade-offs.