The interview process for a freelancer tends to be a 'fast track' version of the one for an employee.
If a recruiter is involved, there will probably be a relatively short talk (hardly an actual interview) with the recruiter, so they feel confident sending you onward to the client.
The client interview is often short (30 - 60 minutes), is very project-centric, almost never involves HR and does not consist of several rounds with a changing group of people.
Almost all questions are technical, allowing you to elaborate on previous relevant experience. At times, there may be 'softer' questions regarding how you react to adversity, unclear requirements and difficult people. This may be a sign of a somewhat challenging working environment.
The interviewer is probably the project manager and/or a senior professional; at times when the project manager is technical enough, they might be the sole interviewer. The recruiter might participate in the interview, but merely as an observer. It seems some recruiters prefer participating - and some clients prefer they do not, as they rarely add any value at that stage. Whether they participate is out of my hands, so I tend to not care.
As a freelancer, I would like to know which exact role is expected of me, which other roles are adequately covered (so I won't end up in them) and what the current challenges are. This line of questioning will be more direct than an employee would (or should?) ask - but is necessary to determine whether the project is a good fit. In addition, I personally find it beneficial to immediately demonstrate that I am a freelancer and not an employee.