When the Governor declares a disaster area, the declaration allows the governor to call upon state agencies to assist counties with response efforts. This assistance would be outside the scope of what the state agencies would do on a day-to-day basis. (An example of this would be the KHP aircraft observation which is underway today. Another example would be asking the Kansas National Guard to provide security or transport equipment or supplies somewhere in the state).
No additional funding is made available to the counties under a state declaration, but rather additional state resources are provided as needed to assist counties when they have exhausted all of their resources. The state agencies providing the assistance pay the cost of providing those resources. (There is an exception with some National Guard assets if they are deployed and those costs are absorbed by the county requesting them).
If a federal declaration is declared (presidential declaration) then money becomes available, if the dollar threshold is met, to reimburse counties and the state for their additional expenses for response.