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A "sort merge" join is performed by sorting the two data sets to be joined according to the join keys and then merging them together. The merge is very cheap, but the sort can be prohibitively expensive especially if the sort spills to disk. The cost of the sort can be lowered if one of the data sets can be accessed in sorted order via an index, although accessing a high proportion of blocks of a table via an index scan can also be very expensive in comparison to a full table scan.
A hash join is performed by hashing one data set into memory based on join columns and reading the other one and probing the hash table for matches. The hash join is very low cost when the hash table can be held entirely in memory, with the total cost amounting to very little more than the cost of reading the data sets. The cost rises if the hash table has to be spilled to disk in a one-pass sort, and rises considerably for a multi pass sort.