Transform relics are items that are ment to transform a maxed legendary item to mythical paired with other legendary items. While ascension relics are items that are used for mythical items to divine. The use of ascension relics might vary depending on what tier you first get the item, for esample : if your item first starts as a rare item, you need to use rare ascension relics, if your item first starts as epic, you need to use epic ascension relics. Those that starts at mythical though would use legendary ascension relics, the same ones you would use when your item that started as a legendary item
Here is a list of ascension relics and how much you would need to use :
Common : 2 relics, used on items that started as common
Rare : 3 relics, used on items that started as rare
Epic : 4 relics, used on items that started as epic
Legendary : 5 relics, used on items that started as legendary, also used on those that starts as mythical
(this info regarding mythicals is unconfirmed, but that is what I know)