Difference between a sub graph and induced sub graph. I have the following paragraph in my notes:

If $G=(V,E)$ is a general graph . Let $U\subseteq V$ and let $F$ be a subset of $E$ such that the vertices of each edge in $F$ are in $U$ ,
  then $H=(U,F)$ is also a general graph and $H$ is a subgraph of $G$ .  
If $F$ consists of all edges of $G$ which have endpoints in $U$ ,then $H$ is called induced subgraph of $G$ and is denoted by $G_U. $  

From here both the definition of a subgraph and a induced subgraph seem same to me..
I can't understand what is the difference between them...
Please help with this..

For an original graph G(V, E), select set of nodes V' from V.
All the existing edges E' that connect between nodes in V' must remain.
This subgraph G' is called induced subgraph.
If you continue to remove some edge from E', then G' is still a subgraph of G, but no longer an induced subgraph of G.
