Still, after all these years, some people don't understand some of these words they throw around.

radioactive material: material that emits radiation
radiation: in this context, alpha, beta, or gamma radiation.

Alpha radiation consists of alpha particles. Alpha particles are identical to ordinary helium nuclei. They consist of two neutrons and two protons. They can cause damage because they are (positively) charged particles. They cause chemical reactions to occur that can damage living cells.

We are normally protected from alpha radiation by the outermost layer of our skin, the epidermis. However, if alpha-emitting material gets into the body--particularly, into the lungs--it will do damage, and continue to do damage, pretty much forever. This is quite likely, eventually, to lead to cancer.

Beta radiation consists of beta particles. These are actually electrons. Like alpha particles, they are charged particles and can damage living cells. They can normally be stopped by a sheet of paper. However beta-emitting material, like alpha-emitting material, can cause continuing damage if it gets inside the body.

Together, alpha and beta radiation are known as "ionizing radiation."

Gamma radiation is very high frequency (and, therefore, very high energy) electromagnetic (EM) radiation. Visible light is EM radiation. Radios, cell phones, microwave ovens, WiFi, and TVs also use EM radiation of different frequencies.

Gamma radiation is whole-body-penetrating radiation, and, because it can interact with the electron shells of atoms, it is also ionizing radiation. In fact, it's that interaction with electrons that radiation detectors exploit in order to detect gamma radiation.

Just being near a source of gamma radiation is enough to be harmed by it--even if the radioactive material emitting it never touches you.

In our submarine, back in the US Navy, there was a spot in the reactor tunnel (used to get past the reactor compartment when the reactor was operating) where a bit of crud from the reactor's main coolant had become lodged in a sample pipe. "Crud" (no kidding) was a technical term defined as "corrosion and wear products in the primary system." That crud contained some cobalt-60. This created a small area, where radiation exposure was higher, that we kept roped off.

The Navy's philosophy was that less radiation exposure is always better. Our limits were set as low as they could be while still being able to operate.

Any contamination with radioactive material at all outside the reactor itself, on a surface, in water, or in the air was considered unacceptable. If it occurred it had to be eliminated immediately. That little pipe was a problem. That place in the pipe was always going to be a low-flow area, and sooner or later some bit of crud was going to settle there. So we kept it roped off with purple and yellow rope with this sign attached.

the reactor tunnel (used to get past the reactor compartment when the reactor was operating)

Actually, there was no way to get past the RC other than the tunnel. The bulkheads around the RC were shielded with borated polyethylene (to absorb neutrons), and no one stayed in the tunnel or near the fore and aft bulkheads of the RC longer than necessary. It's all about minimizing exposure.