Bottom line
Active duty (AD) is full-time military service, and it comes in two big buckets: training duty and non-training duty. Training duty (ADT) is where your AT, your initial schoolhouse pipeline, and other structured courses live. Non-training duty (ADOT) is where ADOS, AR duty, mobilization, and call-ups live. The hard numbers to remember: SMCR AT is at least 14 days (max 15 including travel), and IMA AT is at least 12 days (max 13 including travel).
What it means for you
Most of your active-duty time as a reservist is AT, the minimum block you owe each year. This section defines that block and the other flavors of active duty you might volunteer for or get ordered to. It also lays out the involuntary side: the specific laws under which you can be called up, from full mobilization down to disaster response. You do not need to memorize the statute numbers, but knowing they exist and which one applies tells you what authority an order is running on.