Is there any difference between "closure" and "closing"

Not necessarily. Closing is a verb that can be used in the present or future tense. Closure, on the other hand, is a noun that can technically be used in any tense.

Although in many cases the two can be exchanged freely, closure represents a greater level of finality and significance than closing.

The closure of a store or restaurant indicates an end to its existence as a business entity. Closing might mean the same, but is commonly used simply to mark the end of the daily business cycle.

Closure has several further meanings not represented by closing:

• The emotional state of satisfaction that a situation has ended and will no longer cause stress or discomfort.
• Something that is able to be closed, though it is normally open. An example is a pocket with a zipper. This usage is less common.
• Various meanings in mathematics and other technical fields.

Among other definitions of closure, WordHippo provides the following one:

The collapse of a business. Ex: We have received a very apologetic letter about the closure of the West End Club, but it really left us in the lurch.

Note, however, that "closure" can refer to a temporary state of being closed:

The Mercer Gallery reopened at the weekend after a month-long closure for maintenance and improvements to the lighting system.

(example found on the same site of WordHippo)

As for closing, you will find such definitions as:

The final stage of an extended process or course of events

Or

The act of something that stops

There is however one definition connected to the idea of bankruptcy:

The condition or state of selling the assets of a business, especially due to bankruptcy

And here you can find synonyms as liquidation, shutting down.

At the end of this little "investigation", I would thing that you can say either

The closure/closing (I would add here of the business) took place at the end of last year.

but you will be surprised to find that Gngram gives definite preference to the closing took place.

To avoid ambiguity though, I would simply say:

The business was closed down at the end of last year.

Oxford Languages defines the verb to close down as:

• cease business or operation, especially permanently.

The company closed down some years later.

• cause a company or business to cease operation, especially permanently.

The government promised to close down the nuclear plants within twenty years"