The correct spelling is baling wire, although if you search for bailing wire online, you’ll get near enough the same results. This is because the two spellings have become somewhat (incorrectly) interchangeable, and many companies still refer to it as bailing wire.
Baling and bailing are known as homophones, two words that have separate meanings, yet they sound exactly the same.
Bear in mind, however, that currently, Google will suggest the correction of ‘baling wire’ if you search instead for ‘bailing wire.’
There is also no difference in the product that the words are describing, so one type of wire will not differ in function from another simply because of the name.
The term bailing usually refers to either the releasing of a prisoner on bail, bailing out a bank or an institution (providing it with money to keep it afloat), or to leaving an area (informally).
Baling, on the other hand, often refers to the bundling of goods, the primary function of what baling wire is used for. As a noun, a bale describes a tightly packed bundle of materials like hay, cardboard, or scrap metal. To find out more, you can check out this blog post on bailing wire vs baling wire.