In the PDCCH region in DL radio frame, there can be many places where a specific PDCCH is located and UE searches all the possible locations. The possible location for a PDCCH differs depending on whether the PDCCH is UE-Specific or Common, and also depend on what aggregation level is used. All the possible location for PDCCH is called 'Search Space and each of the possible location is called 'PDCCH Candidates'.
The search space indicates the set of CCE locations where the UE may find its PDCCHs. Each PDCCH carries one DCI and is identified by RNTI. The RNTI is implicitly encoded in the CRC attachment of the DCI.
There are two types of search space : the common search space and the UE-specific search space. A UE is required to monitor both common and UE-specific search space. There might be overlap between common & UE-specific search spaces for a UE
A table from 36.213 shows these relationship as below.