Originally Posted by sailorboy1
It most certainly matters if you plan to quickly CHARGE it and notjust connect it to a house battery that isn't charging.
Compatible battery chemistry is the precondition to proper charging of any batteries in (logical) parallel from the same charging source (otherwise only one battery of the parallel pack will be charged correctly).
Simply connecting the batteries without an active charging source will result in stray currents between the batteries (if connected at different SoC) and unwanted draw from both batteries from any loads attached.
With an active charging source paralleled batteries of the same chemistry the lowest SoC battery will draw down pack voltage, resulting in charge current
mostly directed to the lower SoC battery. Upon reaching the same SoC level, both batteries will accept a fraction of the charge current roughly proportional to their capacities, from that on both batteries will reach 100 % SoC at the same time - as a pack. That means in the „parallel“ scenario there is no way to quickly charge one battery at the cost of charging the other battery slower.
Adding a charge isolator (based on diodes or a „diode simulation“ consisting of MOSFETs protects the batteries and attached consumers from each other (only allowing current draw from one branch of the isolator). In the charging situation the pack still looks like it is paralleled, resulting in identical charge time.
An „echo charger“ type device is slightly more intelligent than simple diodes or MOSFET diode simulations in terms that it switches based on voltage levels. It does not provide a battery individual charging profile to the aux battery voltage and thus does not help to solve the OP‘s problem.
This is why there are two solutions to QUICKLY charging an aux battery in addition to another battery:
1. Disconnect the larger battery from the charging source while charging the aux battery
2. Use a B2B charger for the aux battery
In case 1 it is advisable to have the same battery chemistry.
Case 2 does not care, you program the B2B charger according to the aux battery specifics.