NHL 'systems' are more similiar than many think. basically it usually amounts to more of a change of emphasis and minor changes than anything else in most cases. Haven't watched enough of Washington to know exactly what changes have been made and for some reason couldn't open this article, but the things Trotz emphasised most in his 15 years here in Nashville were;
1)defensive resposibility for his forwards backchecking
2)forwards collapsing more and doubling down in the slot more than many 'offensive' emphasis teams
3)forwards slighter lower along the defensive boards in the defensive zone than most other teams to help clear the d-zone and chip pucks out
4)strong 'emphasis' on forwards being able to win puck battles and chip the puck out of the defensive zone under pressure
5)3rd man high at all times in the offensive zone reducing odd man rushes the other way
6)more man to man coverage in the defensive zone from all his centermen. and in general more defensive accountability out of all centermen in the defensive zone and geting back defensively than many teams.
7)for dmen to only join down low in the offensive end when they were sure some forward was able to rotate back to the point to cover defensively.
8)the defensemen being very careful and responsible when they chose to pinch down the boards in the offensive end to try to hold the puck in.
9)strong emphasis on winning puck battles in the corners from all
in other words, thinking defense first.
but it's impossible to put trotz in a box and say he only coached defensive hockey as many seem to want to do. he was limited many years by the personnel NSH iced. teams with a lack of offensive talent, but good defensemen and goaltending. that's how he had to coach. to be fair, in the years 05-07 when he had kariya, dumont, arnott, radulov, hartnell, legwand, erat and more offensive power he changed his coaching style some because he had offensive talent and NSH was a top 5 scoring team (something people always forget). he still preached defensive responsibility those years though and relied more on being a counter attack offense off the rush from turnovers than being an all out offensive attack team