[Odsh]

According to the FAQ::

Can I upgrade my bioware or cyberware?
Presuming the item in question has not been damaged, you may sell back installed non-cultured bioware and cyberware for a flat 30 percent of its retail value (book price; taking into account alpha or beta mark up, if any) when changing out cyberware. You must still make an Availability test to acquire the new piece of cyberware. Cultured bioware may not be upgraded, only replaced (and no one will buy used cultured bioware, chummer).
Shadowrun Missions FAQ 23
You may upgrade bioware and cyberware by paying the difference between the two pieces of equipment (accounting for grades, if any). You may only upgrade a piece of bioware or cyberware of the same type.
For example, Ramsey wants to get a better Control Rig. He currently has a Rating 2 but wants to upgrade to 3. Whiskey happens to have one in stock and charges him 133,200¥ for the new Control Rig (Rating 3) and keeps the Rating 2 she just pulled out of Ramsey.
So, let’s do the math: Control Rig 3 costs 208,000¥ - 97,000¥ as credit on the old rig (Rating 2) = 111,000¥ for the upgrade.
Another example, Kingston goes to Whiskey and asks to have his dermal plating removed so he can get titanium bone lacing instead. Whiskey gladly obliges, but since these are different types of ware, Kingston only receives 30% of the value of the dermal plating and has to pay full price for the titanium bone lacing.

This is somewhat confusing because the cost of the Control Rig doesn't match the costs in SR6.
Do I understand correctly that:

• When you upgrade an implant to a higher rating and/or a higher grade of the same implant, you only pay the difference (i.e. you sell back the old rating for 100% of its value).
• When you replace an implant by a different type of implant, you can sell back the old implant for 30% of its value.

[Stainless Steel Devil Rat]

I... honestly can't explain that math.  It's something that will certainly have to be looked at and corrected.

Let's just look at the rule and use a different example

New example: After a big score, Sammy the Samurai wants to go from Wired Reflexes 2 (Used grade) to snazzy Wired Reflexes 3 (Alphaware).  The book price for what he's got is 75,000 (wired reflexes 2 costs 150,000, but used grade is half that).  What he wants costs 300,000, including the alpha grade multiplier.  The difference between the two is 300,000-75,000=225,000.  Sammy the Samurai spends 225,000 to upgrade his used Wired Reflexes 2 to alpha grade Wired Reflexes 3.

The 30% value function factors in when you're doing different kinds of augmentations, rather than the same augmentation of new rating and/or grade.  Dermal plating and Titanium Bone Lacing, in that example.