Is that a true six phase or is that like calling 120/240 split phase "two phase" ?
Do you really think a six-phase load cares whether or not the source of the six voltage waveforms used six phase-shifted voltages? As far as the load is concerned, the end result is the same.
Does the method of creation matter to the load as long as it gets what it wants?:
I have a circuit that takes a single-phase source and sends it through a series of delay stages to create a three-phase set of voltages. As far as the load is concerned, the voltages come from a three-phase generator. The main source only sees a single-phase load. The 3-phase end load sees a three-phase source. Single-phase loads see a selection of single-phase sources. It just depends on where you are standing and how you are using the voltages.
How about about a three-phase source serving single-phase loads?:
Think about the 120/240 center-tapped delta bank. Is it a single-phase source or a three-phase source? It can serve as either but we call it a three-phase bank. We can look at what comes into our panel to determine if the panel is single-phase or three-phase. From that point on, it really doesn't matter about the transformer bank, it only matters what voltage waveforms we are using from it.
To take it further, a 120/240 single-phase panel feeds 120 volt single-phase loads and 240 volt single-phase loads so it can take the place of two different type single-phase sources. The 120 volt single-phase load cares nothing about the 240 volt option as long as it gets what it needs. It only needs a 120 volt single-phase supply although ultimately it came from a three-phase transformer bank.
The source could just have easily been a single-phase generator but the load does not care. Even if we had a three-phase generator the 120-volt load would only extract a single-phase supply need.
Consider what you are trying to label:
It makes a difference in whether we are labeling the system that creates the voltages or whether we are labeling the voltages that the load wants.
In the end, if we look at the set of voltages we have and how they are being used, we can classify those voltages in a way that may or may not be the same as the classification we use for the system that created them.
One more example:
One final illustration would be a 4-wire wye bank that only serves single-phase loads. We call it a three phase supply. As far as each load is concerned, it is a single-phase supply. In this use, the three-phase bank is a three-phase load to the system. But, this three-phase bank is actually filling the role of multiple single-phase sources for the loads, and is not filling the role of a three-phase source.
The loads do not care if the voltages came from one transformer or multiple transformers. They do not even care about the phase shift between the voltages because the loads operate independently.
An important note: When they stop operating independently such that the phase shift between their sources becomes important, then as a group they act as more than a single-phase load.