The term ‘hand-painted’ should not be mistaken with ‘hand-coloured’. The latter describes a regular printed item being coloured by hand with or without the use of stencils, airbrush etc. But also when it reads “hand-painted” it is often not unique. Both terms make you believe you have something individual, superior quality to industrial production in hand (and so costs extra).
‘Authentic’ hand-painted cards were often done on standard postcards (some show official postal form imprint like “C 154” in Germany), or just a plain piece of (better/special) card board. Some time after the turn of the century it must had been quite popular, as the shops selling inks and brushes had special postcards one side blank on offer.
True hand-painted cards are individual pieces. There could be (slightly) different versions of same view around. The best examples I have seen come from regular correspondence (= are dated).