Currently, we have integrated the Jira software cloud in our application using REST APIs (Java).
Now we have another requirement from a different customer and their JIRA instance is JIRA Service Manager (JSM).
I need help on the below questions:
What is the difference between Jira software cloud and Jira Service Management?
I already have integration for the Jira software cloud, can I use the same integration for JSM?
While Jira Software (JSW) and Jira Service Management (JSM) are different products, with different licensing models, they can both run in the same Jira site because the unit of difference is a Jira project. From an API perspective, both share the common Jira platform as their core APIs, with specialized APIs to express the concepts specific to those products. As examples (not exhaustive), Jira platform covers shared concepts like projects, issues, and workflow configuration. JSW covers Boards, Backlogs, and Estimation. JSM covers Portals and Requests.
In your case, you indicated you have used the Jira platform APIs, which means the integration will work with both JSW and JSM (and maybe even some future flavors of Jira that have been announced in early access).
Jira Server (with the same APIs that cover Data Center) does have different REST APIs. While somewhat similar, Cloud and Server are effectively different products with divergent REST APIs. The biggest differences are in users (where Cloud has a different identity system), workflow configuration (where there are new kinds of projects in Cloud), and text formatting (Cloud has a new format known as Atlassian Document Format). I advise to threat Jira Server as a different integration target and not to rely on superficial REST API similarities.