Materiel (with an "e") Availability is the NUMBER of operational items divided by the total population. In other words, what percentage of the number of end items are operationally ready for tasking. The total population of operational end items includes those in training, attrition reserve, pre-positioned, and temporarily in a non-operational materiel condition, such as for depot-level maintenance, shipyard repair, etc, typically placed out of operational readiness reporting.
Operational Availability is the TIME those items are available to perform their mission. The formula is the number of hours a group of items is operational divided by the total number of hours (total inventory X 24 hours per day). In other words, uptime divided by uptime + downtime (total time). Typically, many of the assets in categories mentioned as included in materiel availability (training, attrition reserve, pre-positioned, and temporarily in a non-operational materiel condition, such as for depot-level maintenance, shipyard repair, etc.) are not included in the operational availability metric.
Why two metrics to measure essentially the same thing? The JCIDS Manual
https://acc.dau.mil/adl/en-US/267116/file/41245/JCIDS Manual - 19 Jan 2012.pdf ), Appendix E, Encl B, combines the two metrics into one and simply calls it "Availability" or the "Sustainment KPP". The answer to that is that each of the metrics is geared to a specific point of view. If you're the Combatant Commander (CoCom) you need to know how many assets you have available to prosecute the mission in your area of operations. The granularity of operational hours is cumbersome to deal with in this application and unnecessary. Not including out-of-reporting assets would give a false picture. Therefore, you measure materiel availability.
If you're a unit commander (e.g. squadron), you know the number of assets at your disposal but you need to know when they are available. You need to know why specific bureau numbers are down and when they are anticipated back up. Therefore, you measure hours and manage your availability accordingly by the timing of your preventative maintenance or selective cannibalization, etc. The percentage of time each asset is available is critical to your daily operation.