The charger itself only becomes a concern when it comes to the rate of charge relative to battery capacity. That is something tightly controlled by spec and the charging protocol of the phone, so not much of a problem for us.
The 40/80 rule (or perhaps guideline is a better term) has to do with the state of charge. Li-ion batteries become more susceptible to degradation at very low and very high charge levels, regardless of the charging method. In other words, if you set 3 identical Li-ion batteries on a shelf and unplugged, with the only difference being one fully charged, one at 15%, and one at 50%, the 50% charged battery will degrade slower than the other two.
Something else to keep in mind is heat. Heat alone can also degrade a battery, but heat plus a high charge can degrade it exponentially faster. If the phone feels warm to the touch, or you are actively using it, then it's more important to unplug early. The lower the charge level, the less heat will degrade the battery, but going too low is still problematic.
From personal experience, I once killed a battery in about 6 months by keeping it fully charged at all times because I thought I was saving cycle counts. I've had my current LG V60 for just over a year while strictly following the 40/80 rule, and have no degradation according to AccuBattery.