Well, the difference is more function than form. In general, tables are bigger than stands, and typically more generic in function. You have dinning tables, coffee tables, card tables, etc.
Then you have plant stands, candle stands, lamp stands and so on.
Functional tables are your dining/kitchen tables, coffee tables or possibly a computer table. These tables, while attractive, are built for a specific function.
Decorative tables would include end tables or sofa/console tables which are built more for their appearance than their function.
Stands are typically single purpose and often that purpose is decreed. A plant stand is built to hold a plant, though there is rarely any reason why it could not hold a lamp or pictures or anything else.
So, when it come down to a hard definition, there isn’t one.