li-ion battery managment system, cell protection difference?
Cell protection does just what it says: it protects a single cell.

A common chip for single cell protection is the DW01



This chip monitors the voltage across the battery and the current through the MOSFETs. It opens the MOSFETs (which disconnects the battery) when the voltage across the battery becomes too high, too low or when the current becomes too high.

A battery protection circuit protects the battery from harmful conditions. It is not a good circuit to shut off charging when the battery is full. The charging circuit should stop charging before this protection circuit kicks in!

A BMS, Battery Management System isn't designed for protection but for managing multiple batteries when they are connected in series.

When batteries are connected in series and they're charged through the "end" connections (the connections with the highest voltage between them) then all batteries are charged at the same rate.

That's OK as long as all batteries are of the same capacity and have the same amount of charge. When that is not the case, for example one battery has worn out more, then it will be charged fully before the other cells are full. When a cell is full charging MUST stop, at least for that cell. That's what a BMS does, it stops charging that one cell but keeps charging the others so that at the end of charging all cells will be full.

Additional functions of a BMS can be voltage monitoring just like the single cell protection circuit.

Do note that cells wear out and loose capacity over their lifetime. This can be different per cell so you cannot use Li-Ion cells in series without a proper BMS even when all cells are identical (same type, same age etc.).

I only have cell protection when the first cell reaches the desired voltage it shuts down the charge of the entire column, am I right about that?

No it does not and you should not be using cells in series like that, you would be mistreating the cells that way with the consequence that the cells will wear out sooner and an increased possibility of overheating etc. Protection is not the same as the battery management a BMS does.