I work for a "small" institute of the US government which is maybe five steps below a top level US agency (e.g., US department of agriculture, commence, defense, ...). Our director is leaving at the end of the year and staff are now fighting over the merits and drawbacks of appointing an acting director over an interim. What is the difference between the two?
"acting director" is usually someone who is working out of title, such as an assistant director who is taking on the duties of a director until a director is found.
an "interim director" is someone who is working in title, but temporarily until a replacement is found.
Usually an interim director is a director from another department who is filling both roles... I.E. Director of finance, interim director of IT.
Sometimes, a department may have a director move to another department while an assistent director becomes acting director...
So, as in the above example, Bob is the director of finance, but the IT department is a mess, and the director was fired. Bob had been in IT in the past, and can serve as interim director of IT. Bob has his assitant director Alice, fill his role while they look for someone to fill the IT spot....
So, you have Alice, as acting director of Finance, Bob as director of Finance, interim director of IT.
EDITED TO ADD:
The difference between "Interim" and "Acting" is that someone who is "Interim" already has a similar title/qualifications and an "Acting" director is someone who doesn't have the title/qualifications, but is ACTING in that role as if they did.
"Acting" be it "Acting manager" or "Acting director", can be used to get experience in a role before a promotion. Example, after six months as "Acting Director of Finance", Alice is promoted to Director of finance, and is no longer "Acting Director"
Also, (thank you Damila) an "Acting" director may not have the pay of a director, while an "interim" director likely will.
The best way to answer this is probably to ask those staff who are having the disagreement: What do they see as the significant difference between the two? Or are they simply arguing because no one is sure what the difference is?
In my experience, "Acting" means the temporary person is filling in for a Director who has (for whatever reason) taken leave.
The Director may be on an extended vacation, sabbatical, or medical leave. The Acting Director's job is essentially to keep the organization moving until the Director returns. An Acting Director would not normally make any policy changes, and the implication is that things will continue as if the absent Director was still in charge, in terms of strategy and direction.
Meanwhile, an Interim Director is someone who is filling in because the position has been vacated, and a search for a new Director is under way (or will be, shortly).
The person is filling in until a new Director has been selected and has begun working. Interim Directors may also only be responsible for maintaining the status quo, but they are in place with the implication that a transition is under way and things may change once the new Director is in place. The Interim director may be responsible for helping that transition, instead of just maintaining a past Director's strategy.