HLLE scheme is a variant of the two-waves HLL family originally proposed by Harten, Lax and Van Leer (1986). This variant is the positive version of Einfeldt (1988). It is a very robust scheme which behaves as FVS schemes, even if it is originally based on a Riemann solver.
to use in TYPHON: specify SCHEME=HLLE in BLOCK:SPAT_PARAM

HLLC scheme is an extension of basic 2 waves HLL schemes. Slightly different extensions have been proposed by Toro and Batten. All of them provide the third wave resolution which allows this scheme to be accurate in contact discontinuities and boundary layers configurations.
to use in TYPHON: specify SCHEME=HLLC in BLOCK:SPAT_PARAM