Combinational ATPG is applied to designs which are converted into "pseudo-combinational" designs. This is achieved by replacing all the sequential elements with their scan equivalents. This approach is called FULL SCAN
If few or none of the sequential cells are replaced with their scan equivalent cells, sequential ATPG will be employed by the ATPG tool. This is called partial scan methodology.
These algorithms aren't dependent on type of faults, but on the design, as explained above.
There are several pros and cons among these algos, Like Combi-ATPG is simple , lesser run time, pattern size will be less, but coverage might be relatively less when compared to sequential ATPG. Sequ-ATPG employs fault simulation based on time frames, pattern size will be relatively huge, but you can get good coverage.