The stuff you buy in stores should not even be able to be called eggnog.

The best part about real eggnog is you add in whipped egg whites which borderline changes the phase of matter of the drink its light and airy (and boozey) and fresher.

Like you said rhe stiff you get at the store tastes like and has the texture of slightly melted ice cream (not that there's anything wrong with that if it's what you're into)