Interim management is a temporary injection of skills into an organisation.
The Interim will typically work from within the organisation to manage a transition, change or crisis. Because organisations do not need these skills at all times, interim management tends to fall outside IR35. Some interim roles lend themselves to fixed price contracts with payments for achieving pre-defined milestones, goals and benefits.
Freelancers take on specific tasks, most often for a fixed price. The boundaries of the task are clearer and the employment is almost certainly outside IR35.
In my discipline – project management – an interim would enter an organisation that has need of a project but does not need the skills of a project manager on a permanent or fixed term basis. They are likely to spend most of their time within the organisation but will keep a distance so they can be most useful in terms of providing a ‘fresh pair of eyes’. Interim contracts generally last between three and nine months.
On the other hand, many freelancers stand apart from the organisation. They might define a project from business case to schedule, coaching and guiding the delivery manager along the way. They are much more likely to pop in and out of the business and might be able to handle several clients at once. A freelance activity might last an hour or hundreds of hours over several months.
To be honest, the difference is more audience related, I find that larger companies prefer interim and many SME are comfortable with freelance. Both are synonymous with self-employment and contractor.