What are the differences between "eDiscovery Search" and "content search"

Petri-X You are correct in that the only difference would be case access. When using the eDiscovery case, you can assign access to specific eDiscovery Managers. You can also manage preservation within an eDiscovery case. Both Content Search and the search within your eDiscovery case use the New-ComplianceSearch so there is no difference in the search operation.