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What's the difference between an Invalid Application (i.e., due to non-payment of Visa Fee) and a Rejected Application?

Can such an Invalid Application be deemed as Application Never Made or does it have to be referred in the subsequent applications under the questions, 'Have you Ever Applied for Visa' and 'Have you ever been rejected a Visa by any Country', etc.

The question I am specifically asking is in connection with the Australian Visa Application.

Here's a screen shot from the Australian visa application...

If you are filling out an online form, it may look different but the terminology will be the same.

The relevant question on their visa application form is...

Have you ever had an application for entry to or further stay in
Australia refused, or had a visa cancelled?

Terminology is important here. Like most of the Commonwealth, Australia uses "refused" in the same way as our current tag definition...

Also called 'visa denial'. A refused application is a valid
application which has been processed and the decision-maker has
decided that the applicant fails to meet the requirements. Questions
on this tag should include the applicant's nationality and who refused
the application and the relevant text from the refusal notice in order
to clarify the refusal grounds.

They also use 'cancelled' in the same way as the rest of the Commonwealth. It usually means the person got caught inland doing something illegal and their visa was curtailed. It can also happen before the person arrives, but the important distinction is that a visa has already been issued (Schengen uses the term 'revoked'). A cancelled (or revoked) visa is far worse than a refusal unless it was voluntarily revoked.

For other things that can happen, there is the term 'rejected'...

An invalid application that did not reach the decision stage for any
number of reasons: the wrong form was used, or the pictures were not
in the correct format, or the bank declined to pay the credit card, or
countless other reasons that can make an application invalid. When an
application is rejected,, it will be returned unprocessed with the fee
payment not taken or refunded. Compare/contrast to 'visa-refusal'

This type of question does not appear on the Australian visa application form, they don't care about these types of things. So if the fee was never collected for example you can safely (and honestly) deny having made an application. Even if you list a rejection they will see it as such and ignore it.

This answer should be applicable to most (but not all) of the affluent Commonwealth and Schengen. In the USA regime, the terminology is hopelessly inconsistent so this answer does not apply there.

Related: Re-applying for a Schengen visa, difference between 'revoked' and 'annulled'

Another Difference between deportation and removal

'Hippietrail's' seminal question on terminology: Are the terms "visa denial", "visa refusal", and "visa rejection" used in the same standardized way in countries that use English?

Adding as an afterthought...

Disclosing something on a visa application does not result in instantaneous refusal. People put all kinds of weird things on their applications and still get approved: nude photographs, an old flight jacket, microwave parts, ultrasound scans, parking tickets, a jar of nuts, eBay passwords, an autographed dollar bill... you name it. Visa officers are trained professionals who will filter out material that is innocuous, irrelevant, or superfluous. This includes an admission of guilt about something they don't care about.

The definitive answer comes from section 47 of the Migration Act 1958, particularly subsection (4):

(1) The Minister is to consider a valid application for a visa.

...

(3) To avoid doubt, the Minister is not to consider an application that is not a valid application.

(4) To avoid doubt, a decision by the Minister that an application is not valid and cannot be considered is not a decision to refuse to grant the visa.