Basically HD Sentinel performs different disk testing and error-reporting than chkdsk.
HD Sentinel checks the hard disk physical parameters, verifying and reporting any issues (including but not limited to errors related to disk surface).
These include real "bad" sectors and weak sectors which may be re-used (different type of problems related to disk surface). This is a more general verification of working parameters compared to what chkdsk does.
In contrast, chkdsk performs verification of the logical drive(s) only. It scans and fixes corrupted files, MFT/FAT entries, directory entries and so. However, in most cases, when it finds any error (what it call "bad sector") it is not related to physical damage of the hard disk but related only to the logical drive (partition). Such problems usually caused by power failure, system freeze/reset, virus/malware and so - but not really related to the hard disk itself.
Performing a Disk menu -> Surface test -> Reinitialise disk surface test and creating a new partition on the affected hard disk usually corrects the problems reported by chkdsk as then all traces of the previous partition removed and new partition created (on the repaired disk surface).
If there are no problems reported in Hard Disk Sentinel about the hard disk and the operating environment is correct (proper cables, connections used; the operating temperature is correct; the power supply and power line is stable; no system crashes/freezes occur; no overclock in the system), you will probably never see chkdsk.