I am confused on Modern search VS Microsoft Search. I guess, both are same .
Is there any real difference between Microsoft Search Vs Modern Search. I understood OOB search is difference.
Could anyone clarify on this.
"Modern" search refers to SharePoint search. It is just the modern UI on top of the classic SharePoint search we've used for many years.
Microsoft Search is a super-set of SharePoint search with expanded capabilities, but many limitations, too. MSFT Search searches all Office 365 content, has an org chart, and other features, but it lacks the schema manipulation that SharePoint search has as well as the various webparts that you'd traditionally use in SharePoint search.
There's a good overview in the MSFT docs. Overview of Microsoft Search.