FORECHECK SAME SIDE PRESS
The next two forechecking strategies are linked for multiple reasons, not least of which because the initial formations look nearly identical. We'll start with the more aggressive of the two -- the Same-Side Press.
In this forecheck, the penalty kill lines up in a 1-3 formation, with the first forward (F1) significantly ahead of the other three members of the unit, who are positioned in a horizontal line across the ice. The second forward (F2) is stationed in the center of the line behind F1, flanked by both defensemen. F2 usually starts out a bit ahead of the defensemen, for reasons that will be explained soon.
Here is a diagram of the initial look of the Same-Side Press, to illustrate the positioning of the players.
The bulk of the work in the Same-Side Press is done by the forwards. But here, the goal is for F1 to bait the opposition into moving the puck up a specific side of the ice. This lets F2 quickly close in and disrupt the rush, either tying up the puck carrier along the boards or forcing a dump-in. The defensemen skate backwards with the rush, in position to chase the puck if it is dumped into the zone as a result of the press. They also prepare to defend against passes in the neutral zone that try to jump past the press.
Here is a diagram of the Same-Side Press in action.
Same Side Pressure: Flyers use this system
FORECHECK PASSIVE 1-3
The Passive 1-3 forecheck is the less ornery cousin of the Same-Side Press. At first glance the formations look almost identical, except for the fact that F2 often positions himself right in line with the two defensemen rather than a bit ahead.
F1 again puts a degree of pressure on the puck carrier. But in this forecheck, F2 does not race forward to cut him off. Instead, F2 sags back, along with the two defensemen, holding tight at the blue line.
The telltale sign of a Passive 1-3 versus a Same-Side Press is the actions of F2. Generally speaking, if he aggressively moves forward in the direction of the puck carrier, it's a variation of the Same-Side Press. If he skates backwards or remains in the center lane waiting for the play to come to him, it's likely a Passive 1-3.
The lack of activity from F2 places the onus on either F1 to disrupt the rush, or the defensemen to stand up the puck carrier at the blue line and force a turnover or a dump-in. Here is an example of the latter.
FORECHECK RETREATING BOX
There are a few NHL teams that incorporate the Retreating Box system as their main forechecking schemes. Unlike the Same-Side Press and Passive 1-3, it's immediately obvious from a structural standpoint when a team is using the Retreating Box formation. A change of pace from a 1-3 formation, the Retreating Box is more of a 2-2.
The key to understanding the Retreating Box from a structural standpoint is to think of it as a literal rectangle retreating down the ice. The horizontal invisible line made by F1 and F2 stays parallel with the line of D1 and D2, and the same goes for the vertical lines of F1/D1 and F2/D2.
However, this only holds until the puck gets in range of the front of the box (F1 and F2), which usually occurs around the red line, kicking off the pressure portion of the forecheck. Remember how the Same-Side Press baits the puck carrier into going up the sides before trapping him? The Retreating Box has a similar concept, daring an opposing power play to use the center before surrounding the puck carrier once he commits.