According to my understanding, s3c2410 is processor.smdk2410 is machine that use the processor s3c2410.
Please see s3c2410x_mach_init[skyeye/arch/arm/mach/skyeye_mach_s3c2410x.c], you should get the mach-type of your machine.
void
s3c2410x_mach_init (ARMul_State * state, machine_config_t * this_mach)
{
ARMul_SelectProcessor (state, ARM_v4_Prop);
/* ARM920T uses LOW */
state->lateabtSig = LOW;
state->Reg[1] = 193; //for SMDK2410
//state->Reg[1] = 395; //for SMDK2410TK
//state->Reg[1] = 241; //ARCH_S3C2440