Can anyone please tell me with an example what production materials, production and service parts mean in the definition for supplier? Does it include suppliers of stationery items, coolants etc.?

Not unless you use those materials in the production of the parts you are supplying.

This does not include office supplies, computers, food service in the break room, utility suppliers (electric - gas - water), desks and furniture, company cars, mops, buckets and other cleaning materials for the shop, maintenance supplies, duct tape, screwdrivers and wrenches, and hundreds of other things used in the course of doing business.

Hope this helps.

Dave

This does not include office supplies, computers, food service in the break room, utility suppliers (electric - gas - water), desks and furniture, company cars, mops, buckets and other cleaning materials for the shop, maintenance supplies, duct tape, screwdrivers and wrenches, and hundreds of other things used in the course of doing business.
In the largest sense, these are all suppliers, however.

Who do you write checks to?

'Checks' (who do you pay) do not address internal suppliers.