I often get questions from consultants asking me, "What's the difference between my interview with a recruiter and the interview with the client (hiring manager)" or "Why do I need to meet with you if I'm also meeting with the hiring manager?" There is a real difference between the recruiter interview and the hiring manager interview, and they each have their importance. Remember, the recruiter is a third-party individual who is working with the client company to go out into the market and find the best candidates possible for that client company's position. The hiring manager is someone who actually works directly at the client company seeking to fill the position.
A recruiter is requested to use their searching expertise to go out into the industry and find and qualify the best candidate possible who specifically fit a set of requirements provided by the hiring manager. They're really focusing in on skills and requirements and the job fit. It's the hiring manager who will take this candidate from the recruiter and then determine if the candidate's qualifications are suitable for the open position, the team fit, the company's culture, the company's core values, etc.
An interview with the recruiter is important. In this interview they will ask you questions to help them determine if you have the specific skills required for the open position. The recruiter wants to set you up for success in your future role so they are going to look deep into your work experience and try to understand both your strengths and weaknesses. Interviewing with the recruiter is also good practice. As per this SparkHire post, during this interview, the recruiter will also coach you and help you prepare for your interview with the hiring manager. They will provide you with useful tips throughout the hiring process, such as appropriate dress, resume format, and handling gaps in employment. They can also provide advice on when it's appropriate to ask questions about things such as salary and benefits. Your best bet is to look at your interview and conversations with the recruiter as more of a training advantage and a way to learn inside information on the job and hiring manager beforehand.
During the interview with a hiring manager, the hiring manager will ask you questions to determine if your experience would be beneficial not only to the position but to the company as well. The hiring manager is the person who defined the scope of work, including the tasks and responsibilities, and the requirements of the role. They also have the bigger picture and understand the goals and milestones that go along with this role. The hiring manager has the insight into the company and is more likely to assess your skills to see if your skill set would align to other projects or departments in the company, along with this position. They are also asking the candidate questions to determine the team and culture fit. It is the hiring manager who makes the decision over whether or not to hire the candidate.
Remember, it's important to create a good relationship with your recruiter. A good recruiter is an added benefit to your job searching. If this particular opportunity didn't work out and if you've made a good impression, the recruiter will work with you on future positions, increasing your options.