Yes, the BMS does the management of the li-ion charge, though the charger needs to sense the full charge cutoff and change it's charge and indicator LED state accordingly. Maybe SLAs read differently from the charger's point of view.
.
They certainly do. A Li-Ion charger for a 37V battery just puts out about 42V and usually current limits to whatever its rating is. The battery's BMS does everything else within that limit.
In order to indicate 'full' a Li-Ion charger just needs to sense the sudden sharp drop in charging current when the BMS detects that the battery has had enough. I haven't done any specific checks but I suspect that a much reduced charging current may flow for a while after that to allow for cell equalisation, etc,
If you plug a Wisper Li-Ion charger in to the mains and switch it on with no battery connected, you get a green light right away. It doesn't know whether a battery is connected or not, and just sees that no current flows, therefore the battery is full as far as it can tell.
SLAs have no built-in management system. You can charge those with a constant-voltage charger which also current limits to prevent itself being overloaded by a flat battery. The usual voltage to achieve a full charge without over-charging an SLA is around 13.5-14 volts per 12 volt battery.
As the battery reaches full charge its terminal voltage rises and the charging current automatically drops to a few milliamps, so it's self-controlling, and leaving the battery connected for a while after this point is reached does a good job of equalizing the cells.
It's an interesting coincidence that the constant-voltage charging requirement for a 36V SLA is also about 42V (3 x 14V) so quite likely the SLA version of the charger mentioned is very little different to the Li-Ion version, except possibly in the circuit for detecting a full charge, since an SLA's charging current tails off over time.
There are more sophisticated ways to charge SLAs - if anyone is interested, I'd be happy to elaborate in 'The Charging Post'!
Rog.