When we talk of radioactive substances, the main three types of radiation are alpha radiation, beta radiation and gamma radiation.
Alpha radiation is the radiation of a particle which can only travel a very short distance, except in a vacuum. But if an alpha emitting substance is inside your body it will do a lot of damage.
Beta radiation can travel further in air. It is a much smaller particle, and does less damage inside you than alpha, but more than gamma.
Gamma radiation can travel through almost anything (except thick lead), but the particles are very small. We are all being hit by some gamma radiation all the time. In high doses it is deadly. When your body is hit by gamma, a small proportion of the gamma is stopped: it is that portion that is stopped that causes the damage, the majority that passes straight through does no harm. And our bodies can cope with/repair small damage.
Diagnostic medicines are given containing gamma emitting substances for the purposes of performing scans. The type of substance given would be one with a short half-life... long enough to have the scan. Because it is a fairly small amount of gamma radiation the benefit to the patient outweighs the risk of damage.
You could have a ton of alpha emitting substance sitting in your living room and it probably would do you no harm until you started to crush it up and inject it inside you. But if it was a high-dose gamma emitting substance you wouldn't be reading this.
Smoke detectors use alpha radiation. When buying a smoke detector for installation, remember that as long as you don't try to crush up the smoke detector and try to eat it or inject the tiny amount of emitting substance, a life insurance policy probably isn't necessary. Finally, it isn't a good idea to break the detector, crush up the emitting chemical, get it somehow into a liquid, and inject into the wife (or husband), because it would be tricky to explain it away as an accident, either to her or, in the preferred scenario, to the legal authorities.