A company is a concept defined within Google's configuration and contract.
A payment integrator account ID correlates with an agreement (contract) that the payment integrator has signed. A payment integrator account ID will define things associated with capture and refund: purchase currency, settlement currency, minimum transaction values, etc.
For more details, see the Company and Payment Integrator Account ID glossary definition.
The company defines things such as keys, URLs etc about the particular connection between Google and the payment integrator.
The structure of a company having one or more accound IDs allows Google and the integrator to structure fees and eligibility independent of a user adding their instrument. Further it allows all instruments created within the company to work on all payment integrator account IDs.
The Association flow contains a subtlety that needs to be called out. Google Payment Tokens and association IDs are not associated with a particular payment integrator account ID. They are associated with a company. All GPTs must be automatically associated with every payment integrator account ID within the company. That doesn't necessarily mean every GPT will be useable in every purchase flow for every payment integrator account ID within the company. For instance, if a particular payment integrator account ID specifies a currency code that isn't supported for a purchase, the capture must fail with an error.
Companies and payment integrator account ID have a 1:N relationship, where N is >=1.