As the name - surface printing - suggests, ink is used on the top of films for printing purposes. This is an old printing method for stand up bags. In this printing process, the artwork is continuously exposed to the atmosphere. A downside to this approach is that constant exposure to degrading environmental factors takes the shine out of the artwork. Rough handling can flake off parts of printing, thus reducing its attractiveness over time.
Trapped printing works differently. Typical custom printed pouch bags are made from several layers of film. Each film has its unique function in the structure. Artwork and product information are printed on one of these films. The layers on top of the printed film are transparent. This approach to printing has two advantages. First, it prevents moisture, air, dirt, and oxygen to react with printing and consequently make it drab. Secondly, transparent layers make it nearly impossible for artwork to flake off; rough handling never touches the interior - trapped - print layer which carries the artwork.
Therefore trapped printing is better than surface printing because it keeps the artwork looking new for longer periods and safeguards its attractiveness.