Two continuums, two axes:
“Present” is how an organisation presents itself outwardly to the world, to potential employees, to potential customers, to initial enquiries, to regulators, to potential funders etc. “Behave” is how an organisation behaves with someone or a situation inwardly, once they are part of an exchange or interaction – to established employees, to regular customers, to enquirers who have returned for more dialogue, to the contact people working for regulators and funders looking to make their lives and yours easier.
“Formal” is about structures, forms, procedures, hierarchies, doing things ‘properly’. “Flexible” is about getting the job done, bending the rules, making the customer/employee/regulator/funder happy even if it means doing things differently, doing the right thing by ignoring the printed manual.
You need the “formal” as a skeleton structure and a starting place, and it gives everyone confidence about where they stand, and where you are going. But if you “behave” like this, people are stifled and frustrated and all eventualities are not catered for.
If you “presented” as “flexible”, it would be unprofessional, unfocussed, unmotivating, and you wouldn’t get funding or contracts as other organisations’ structures couldn’t see how you tick their boxes.
So, “present” as “formal” and “behave” as “flexible”.