You have triggered a multi-barrel question not specific to what kind of statutory compliance. Whether in the case of ESIC, Form 16 is an accidental report from the employer, and it differs from act to act. Anyhow, when the Finance department intervenes, I got you as "Form No. 16 A" with respect to both HR and Finance departments. It is TDS (tax-deductible sources) for yearly filing from April to March, levied upon employee salary sources covered under the IT act, containing taxable and non-taxable items as part of the salary.
Most organizations' Finance department will look after this part since Exercise & Accounts/Income Tax are their concerned sections, which are classified. However, a good HR should keep an eye to protect the company as well as his employee staff from falling into the hands of excess tax deductions. Read and learn more facts on taxable and non-taxable benefits and be more comprehensive with pay/wages.
Best of luck,
Kalyan