Is it accurate to describe these radiation measurement units in terms of where-it's-measured and relationship-to-time?
Maybe some numerical values may help.

Radioactivity. The activity is the number of disintegrations occurring per second in a given source. The unit is the Becquerel : $1 Bq = 1 s^{-1}$. For example, the experience shows that $3.7·10^7$ nucleus are decomposed per second in $1$ g $\ce{Ra-226}$. The activity of $1$ g $\ce{Ra-226}$ is $3.7·10^7 Bq$ which was previously called $1$ Curie ($1$ $Ci$). One Curie is a huge activity for usual measurements in the laboratory.

Exposure dose. If a gamma-ray radioactive source is in air, the gamma rays ionize the air around. As a consequence, they deposited some energy in a small volume of air situated at a distance from the source. If the small air sample is far away from the source, the amount of energy is smaller than if it is near the source. The amount of energy so absorbed by the air sample is called the dose (or exposure dose) and is determined with dosimeters, and it is measured in $J/kg$ air. The unit of dose is röntgen ($1~r$), equal to $0.01 J/kg$.


The experience shows that $1 Ci$ of a gamma-ray emitter delivers a dose of $1$ röntgen per hour ($1 r/h$) in air at $1 m$ distance from the source. This value is  somewhat dependent on the nature of the radioactive source. Let's forget about this difficulty for the present purpose. Most important, the dose decreases with the square of the distance. So, to be consistent with the units, the dose delivered by a gamma-ray source is $1 r·m^2 Ci^{-1} h^{-1}$. A small volume of air (some milliliters) situated at $1 m$ distance from a $1 Ci$ gamma source, absorbs in one day ($24 h$) a dose equal to $(1~r·m^2·Ci^{-1} h^{-1})·1 Ci·24 h/(1 m)^2 = 24~ r = 0.24 J/kg $. This energy is finally transformed into heat.

If the irradiated matter is not air, but another substance, like water, the amount of energy is called absorbed dose and is expressed in Gray, abbr. $Gy$ ($1 Gy = 1 J/kg$). The experience shows that an exposure dose of $1$ röntgen delivers an absorbed dose of $0.01 Gy$ in water, like in air.

Living tissues are mostly made of water. But they don't react the same way to a given absorbed dose. Some molecules like ADN are much more sensitive to a given adsorbed dose than water. To compare the biological effects of a given dose expressed in Gray, it is necessary to define a new parameter, the effective dose, which is expressed in Sievert, abbr. $Sv$. $1 Sv = 1 Gy$ in water. But $1 Sv$ = up to $20~Gy$ in sensitive tissues.


The present explanation is just a first approach of the domain of dosimetry and radioprotection. As quickly mentioned in the text, the energy deposited in a target depends also on the energy of the gamma ray, which was forgot here. And we have not spoken about alpha and beta rays, whose dosimetry is not similar to gamma rays. Dealing with these problems should take hours, and cannot be done in the present message.