Helmet, climbing helmet or bump cap?
A safety helmet according to EN 397 is designed to absorb falling objects and sits loosely enough to pop off your head on impact. A climbing helmet according to EN 12492 has a sturdy chin strap that keeps the helmet in place if you fall yourself, and also protects at the sides. A bump cap according to EN 812 is not a helmet: it only protects your own head against a beam or scaffold plank.
Adjusting and combining
Adjust the harness so the helmet sits level on your head and doesn't slide backward; otherwise your forehead is unprotected. If you also need hearing protection or eye protection, choose versions that fit the same helmet. Replace the helmet after any hard impact and observe the manufacturer's maximum service life; the production date is stamped in the shell.