What's the difference between $E(K)$ and $E/K$ in elliptic curves? For a field $K$, sometimes I see elliptic curves denoted as $$E(K) : y^2 = x^3 + ax+b$$ and other times as $$E/K :y^2 = x^3 + ax+b$$

What is the difference? I believe that $E/K$ denotes that the coefficients $a,b$ are pulled from the field $K$ only, whereas in $E(K)$ they may be pulled from the algebraic closure of $K$. Is this correct? I.e. if $\bar{K}$ is the algebraic closure, then $E(K) = E/\bar{K}$ ? Also, is the $E/K$ notation at all related to the notation used for extension fields or quotient groups?
The notation $E/K$ means that $E$ is an elliptic curve defined over the
field $K$.

The notation $E(K)$ refers to the group formed by the points on $E$
with coordinates in the field $K$.
The set of points of $E $ is a group,  with addition defined geometrically. ..$E (K)=\{(x,y)\in E|x,y \in K \}$ , for a field K, is a subgroup of  $E $,by a theorem of poincaré...(my interpretation is that  $E $ is originally taken over a field $L $, where $L $ is an extension of  $K $.)