I noticed some games use the term Powerslides and others use Drifting, but is there a difference?
I mean generally, not specifically to single game. Some games call the action Powerslide and some call it drift. For example, Crash Team Racing calls it Powerslide but Burnout 3 Takedown calls it drift.
In short, a drift starts before the apex of a corner while a powerslide starts behind it.
While dly's answer covers the more technical definition of the terms, I thought I'd address some points specifically about CTR, as the concept is slightly different in that game.
You can go faster through turns by power sliding. To access the power slide, press and hold the R1 button while turning hard.
A crucial maneuver in Crash Team Racing is the power slide; the player executes the slide by holding down one of the shoulder buttons to perform a hop, and steering before the kart lands.
The power drifting is also very different from Mario Kart, where instead of drifting until you get a colored spark to tell you 'Let go to move fast' you rather use one trigger to drift and the opposite trigger when the drift bar is green. You can do this up to three times and it makes drifting so rewarding in CTR.
Powerslides and drifting also took a notable upgrade in CTR. Drifting around turns has almost always been a simple way to get a small boost since Mario Kart 64 in 1996. However, Crash Team Racing was the first to explore the concept of the powered-up boost. Drifting around corners built up a boost meter and toggling a boost just before a catastrophic spin-out would allow players to score a better version of the regular boost, making drifting a special exercise timing and precision.
Note that the 'boost' mechanic is a separate action to a Powerslide. It's known as Turbo Boost in game, or sometimes 'Drift Boost', 'Slide Boost' or simply 'boosting' by the community. It's worth mentioning but it's a large enough topic all to itself so let's just focus on the slide part of the mechanic here.
I can't speak for Burnout as I've never played it, and I'm sure more simulation-racing games like Gran Turismo probably differentiate between the terms in the manner described by dly's answer, but for CTR specifically? There isn't really a difference. You should be ok to use them interchangeably in this context.