Not much different than it is now. Batteries are used by a large number of industries in a wide variety of products and mind bogglingly vast sums of money have been spent on improving them for the last century.
Most applications don't have the same requirements as in a car though. A car battery has to be portable, as light as possible, survive frequent charging and discharging, charge relatively quickly, handle significant weather differences, be resistant to catching on fire, and I'm sure I'm missing some factors. Most other uses only need a subset of these, and also the scale is not as large as it would be if we electrified every car. (Ideally we move away from cars in general, but we should work on both of these.)
Sorta. This thing was basically a horse carriage with an electric motor. If you build it light and don't expect it to go much faster than a horse at a trot, then yes, you can have a perfectly functional electric car with decent range way back then.