Sodium and chlorine from normal table salt (NaCl) are dissolved in water as ions (charged Na+ and Cl-) so they are already separated by many H2O water molecules.
Sodium metal is in a crystalline matrix with no water in between the Na atoms. When in contact with water it wants to react violently with water with the following formula:
2 Na (solid) + 2 H2O (liquid) > 2 NaOH (aqueous) + H2 (gas)
which then once the reaction is complete the Na from the sodium hydroxide are now all dissolved as cations in water separated by many H2O molecules like the NaCl
Likewise, the Chlorine gas that is dangerously toxic to humans is in the form of Cl2 (Cl-Cl) and this has biochemical reactions that I do not understand (inhibit some required function in body upon inhalation), whereas the Cl- anion is dissolved in water and will not turn into the chlorine gas spontaneously, but, for example, adding an acid to bleach (sodium hypochlorite) is very dangerous as it can produce chlorine gas.