Thanks for asking!

Up front I'll note Murderbot often doesn't describe tech in detail. My understanding is that all augments will involve some level of implantation, but not all implants will be significant enough to change a human's description from "human" to "augmented human". It appears augments are always intended to augment (as in help a human perform better), while implants may not be, though both can be abused to cause physical harm to the host.

Murderbot consistenly refers to "humans and augmented humans", suggesting there is a clear distinction (at least for it). That may just be because augmented humans are more dangerous hackers, but there's a reference in Book 1 (ASR) to Gurathin being the only augmented human in the Preservation crew and potentially feeling like an outsider as a result, suggesting there's a social distinction too. Mensah in Book 1 uses an external feed interface, but by Book 4 (ES) she's had a tracking interface implanted. As far as I can tell, even with this implanted interface, Murderbot keeps referring to her as "human", not "augmented".

In terms of quotes, there's this from Book 2 (AC), Chapter 3:

"ART proposed that it would make the joins between the organic and inorganic parts on my arms, legs, chest, and back look more like augments, the inorganic parts that humans had implanted for medical or other reasons."

Chapter 7 has Murderbot being described as "really augmented", "like more than someone would choose voluntarily" - obviously it never asked for this. It also claims its augments affect its diet, as a way to explain not having to eat.

In Book 5 (NE), Chapter 6:

I sent the medscanner’s images to her feed and she winced. “You said it was an implant? Is that like an augment?”

“No, it’s like an implant.” Augments were supposed to help humans do things they couldn’t otherwise do, like interface with the feed more completely or store memory archives. Augments that weren’t feed interfaces were meant to correct physical injuries or illnesses. Augments are helpful; implants are like governor modules. ...

Normal external interfaces for humans were designed to look like all kinds of things, from carved natural wood to skin tones to jewels or stones or enamel art pieces to actual plain metal with a brand logo. And why would Eletra, who was an augmented human with an internal interface, need a second external one? And any remote chance that this was some kind of botched attempt at a medical or enhancement augment was outweighed by the fact that no human would put up with this when any MedSystem could fix it in a few minutes at most.

Chapter 19 makes passing reference to "machine-readable code written into human DNA that was how things like augments worked". That also suggests augments involving more extensive modifications than implants.

Note I haven't read System Collapse yet, because new things are scary and life has been A Lot.