what is different between database clustering and database partitioning
A clustered table1 stores its rows in the physical order that matches the logical order. To do that, the clustered table has no heap at all, and instead stores its rows in the B-Tree leaves. This can benefit certain kinds of range scans tremendously. For more info, take a look at Use The Index, Luke!
A partitioned table is split to multiple physical disks, so accessing rows from different partitions can be done in parallel.
A table can be clustered or partitioned or both (depending on DBMS).
1Also known as "index-organized table" under Oracle. BTW, Oracle cluster is different thing from Oracle index-organized table.
In simple words, If you have too much data then you have to partition data on the different machines so searching can become fast and Clustering is the process that sorts data in the partition.