This question can refer both to whether a project is company-managed or team-managed and the particular Jira product the project uses.

You can find this information for each project on your View all projects page: <your site name>.atlassian.net/jira/projects

The following is some information on the various product names and what you can expect to see for each in various areas of the site.

Jira Service Management (JSM)

• Previously called Jira Service Desk
• JSM projects will have a URL that contains “/servicedesk/”
• In a site’s View all projects page JSM projects will show Type: Service management

Jira Software (JSW)

• JSW projects will have a URL that contains “/software/”
• In a site’s View all projects page JSW projects will show Type: Company/Team-managed Software
• JSW and Jira Work Management are sometimes bundled* 
• Side note: JSW projects can user either a Scrum or Kanban board

Jira Work Management (JWM)

• Previously called Jira Core
• JWM projects will have a URL that includes “/core/”
• In a site’s View all projects page JWM projects will show Type: Company/Team-managed Business
  
• Jira Software and JWM are sometimes bundled*

*Sometimes “Jira Software” refers to the bundling of both JSW and JWM products. JWM is included as part of the JSW licence but not vice versa. Therefore some customers will only see JSW in their subscriptions but will have projects that are both JSW and JWM.