Are you able to give a breakdown of the different abbreviations, so I can better understand the data presented?
Sure. All this information is taken from the NHL's individual plus/minus data (which for each player has the total goals with them on the ice, the total power play goals for with them on the ice, as well as the total goals against and the total power play goals against with them on the ice). That is combined with team totals for each season (total goals, total power play goals, and so on).
That's where the usage metric comes from, because we can look at the total team goals at each game situation and figure out how many of them came with the individual player on the ice. For example, in 1982-83 Wayne Gretzky was on the ice for 77 power play goals for and 35 power plays against. The 1983-84 Edmonton Oilers scored 86 power play goals and allowed 89 power play goals against, so we can calculate that Gretzky was on the ice for 90% of his team's power play goals and 39% of his team's shorthanded goals.
It should be noted that this doesn't necessarily correspond exactly to ice time, since Edmonton probably scored at a higher rate with Gretzky on the ice than without, so it is very possible that he only played, say, 80-85% of the ice time or whatever, but this is the best estimate we can come up with from the available data, and as long as we are comparing elite players to other elite players then that error should largely wash out and we will therefore have pretty good estimates.
TmPP+ and TmSH+ are team metrics that rate a team's success on special teams, including shorthanded goals. Again, looking at the 1982-83 Oilers, they scored 86 power play goals while allowing 6 shorthanded goals against, for a net goals for of 80 in 294 power play opportunities. The average team that year had 71 power play goals and 9 shorthanded goals against, for a net of 62 on 310 chances. Adjusting the Oilers to a league average number of opportunities bumps them up to 84 per 310 opportunities, and then 84/62 gives a TmPP+ of 1.35, which indicates an outstanding power play unit (35% more effective than average).
On the flip side, the Oilers allowed 89 goals while shorthanded, compared to the league average of 71. However, the Oilers also scored 22 times (average was 9), and the Oilers had to kill off 396 power plays, while the average team had only 310. That means Edmonton was a net 67 goals against in 396 chances, which pro-rates to just 52 in 310 chances. The average team was net 62, which gives the Oilers a TmSH+ rating of 0.84. Less than 1 is better for the shorthanded numbers, meaning they were 16% better than an average team.
Note that these are team ratings, for the entire team not just when a specific player is on the ice. An individual player can absolutely impact them, especially if their usage rate is very high, but at the same time they can only do so much as a member of a 4 or 5-man unit.
$PPP and $SHP are a player's points in each game situation, adjusted for scoring environment, games played and level of league power plays. This is pretty much just like any other adjusted points stat, except for the additional factor of a team's individual power play chances for/against. For example, Gretzky scored 54 power play points in 1983, which adjusts to 48 $PPP. In 1989, he had 53 power play points, but that adjusts to just 38 $PPP, mainly because we'd expect him to score more given that the average team scored 85 power play goals in 1989 compared to 71 in 1983, and because the 1989 Kings had slightly more opportunities compared to league average than the 1983 Oilers. $SHP works the same way, except for shorthanded points.
I've also done a bunch of posts about adjusted even-strength plus/minus, that calculation is done by taking a player's individual plusses and minuses, adjusting for shorthanded goals for and against based on their usage stats, and then subtracting them from the team's overall even strength goals for and against. That gives us a "on-ice" number of even strength goals for and against for each player, and an "off-ice" number of even strength goals for and against with the player either on the bench or in the press box. Comparing those ratios gives us the sense of whether a player was better at outscoring relative to the rest of his teammates. Obviously this stat is influenced by a player's linemates, how the coach used them, how good the rest of their team was, and so on, but it is at least one way to look at a player's overall impact beyond just counting points.