"Functionally grounded" is a term that originated in the 2017 NEC, that essentially made most systems fit this term. Even systems that were previously distinguished as grounded and ungrounded, both get considered functionally grounded from 2017 and later. It ultimately means that there is an indirect reference of the DC side of the system to ground.
The kinds of systems that are not functionally grounded would be
1. Systems that are solidly grounded
2. Systems that use non-isolated inverters, and are connected to ungrounded AC grids.
Since most grounded systems use a GFCI method to bond the grounded polarity and EGC, rather than a solid bond, these classify as functionally grounded. It is rare that a grounded system has a solid connection to ground, since GFCI has been a requirement for decades, and this was the way it used to always be done. These become ungrounded and turn off the inverter, when there is a ground fault. Under ordinary conditions, these have one polarity grounded, and the other polarity live, and generate a waveform with one of its peaks at zero, rather than a waveform that is symmetric. To remove the DC offset, they integrate a transformer in the inverter, so that the output can be symmetric about ground.
Systems that use non-isolated inverters were previously known as ungrounded, and are now called "functionally grounded" (I don't agree with this term in this meaning, but it is what we have) when connected to a grounded AC grid. The functional grounding happens means of not isolating the DC side from the AC side, such that the DC polarities are equal and opposite about ground, in order to generate the positive and negative halves of the waveform. The inverter doesn't need an isolation transformer, because the waveform doesn't start with a DC offset.