Closed and private job openings are not the same! Both are seen as active jobs and take up a job slot, but there is a slight difference:
A closed job means you've closed the applications for your job and don’t want to receive new applicants anymore. You're ready to plan interviews with candidates and go through the hiring process with your current batch of candidates.
A private job post means the job opening is not visible to the public. For example, because you're hiring internally. You can share a unique private link to this job post, so people can visit and apply.
Most companies publish their job posts open to the public. When they have enough applicants, they close their applications, and start reviewing and communicating with candidates. When they've hired someone, they finally archive the job.
For a complete overview of all different job states, read the article about Homerun's job states.