The calibration of the TDS meters will be slightly different, however, the TDS meter works by transmitting an electrical current in the water. Electricity cannot pass through purified water - only through water with dissolved solids in it.
So your TDS 000 is to be trusted. If your pure water had solids in it; even a tiny amount; you would get two different readings on your TDS meter such as (for example) TDS 10 and TDS 23.
I wouldn't worry at all, if I were you.