if you add a induction heater on a temperature controller you basically turn a kettle with biab into a aio
the biab is def simpler cheaper and less stuff involved but the temp control mash makes a diff imo
I'm a broken record, but..... "BIAB" does not describe anything about a system other than the fact that the mash is contained within a bag or a basket (take your pick if BIAB is strictly a name for a bag system if you want to). The main property is that the mash is performed inside the boil kettle and the grain is removed from the wort which remains in the boil kettle. That's it.
It does not describe:
1. how the kettle is initially heated.
2. how the mash temperature is maintained.
3. how the mash temperature is raised.
4. whether the mash liquor is static, stirred, or recirculated.
5. how the bag/basket is lifted and/or suspended in the draining position.
A BIAB system can be direct fired on a flame. It can be heated with induction or immersion style elements. It can be recirculated. It can be stirred. Sky's the limit.
An "All in One" is basically a marketing term for a fully packaged system with electric heat, grain basket, controller (and sometimes chiller and/or pump). One could make a system from DIY or commercially available components but we're less likely to call it an AIO, though it functions similarly and sometimes at higher performance.