Cloud is more and more used to deliver IT related services under the form of software applications and systems
A comparison between Cloud software (SaaS) and classical Software licensing:

As a form of delivery of software, the difference is whether what is delivered is a tangible product or not. SaaS is not a tangible product (as compared to software licensed with deployment on client side including executable files than depend on client’s operating system, with the licensor wanting to control how many copies of software are distributed and all that stuff).
Multiple users are also possible with SaaS, I would say there is no limitation (except maybe the server capacity of Supplier to service thousands of users or so that could access SaaS concurently).
From the perspective of associated services, there is no maintainance, but still training and support is the case. Also, disaster recovery / business continuity, but this is no longer on client side, but in Supplier responsibility. This difference is important.
Another important topic remains a Service Level Agreement. This establishes a minimum level of availability of service that the Supplier must comply with as for the Client to be able to continue the work during its working hours. Important is also the network communication. It needs to be secure enough, as opposite to Software licensing whereby the software can work locally and is less exposed to Wild Web – and this is in case the business model does not imply links to other business partners (but very few cases, though, as nowdays we live in a connected world).
As far as accounting treatment is concerned, SaaS is different than software delivery under the form of some tangible product, because SaaS is rather an expenditure which goes on P&L, as compared to a tangible product such as software which goes on Balance Sheet of client (intangible assets) and only depreciation goes to P&L, but progressivelly during the lifetime of the delivered software product. There are pros and cons to each alternative from accounting view.
As far as payment is concerned, both software licensing and Saas could have various fees arrangements. For SaaS there is common the subscription fees structure or even fees per client transaction. Software licensing could also have various arrangements, but I don’t think a fee per transaction is usual as it might be applicable for SaaS (in rare cases, though).
Finally, there is no possibility to copy or redistribute software in case of SaaS, which it cuts off all stuff with copyright and control of licensor going to licensee premises and auditing about how many utilisations or users have using the undelying software product, if complying with number of licenses, etc.
Pros and Cons above should be carefully assessed when analysing the opportunity between the two alternatives.
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