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I mean, the, whatever type of creature this thing is, is an Electric- and Poison-type. It doesn't get STAB on Boomburst. On the other hand, it doesn't really have a very flashy movepool so aside from that, are there other reasons why this thing runs the move or is it simply the lack of alternatives? And speaking of, is there any notable difference between its two forms? I checked its stats and abilities but there doesn't seem to be any difference aside from appearance

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You'll probably get a better answer by asking here: https://www.smogon.com/forums/threads/simple-questions-simple-answers-thread.3656259/
https://bulbapedia.bulbagarden.net/wiki/List_of_Pok%C3%A9mon_with_form_differences says that the Toxtricity forms have a different ability and 2 different level up moves.
Boomburst doesn't have STAB yes, but it gets a 1.3x boost due to Toxtricity's ability Punk Rock. It's generally to hit Ground-types hard (eg. Landorus-Therian) and probably the best special coverage aside from STABs.

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Boomburst is Toxtricity's strongest attack (calc). This is because Boomburst has 140 power compared to 95 on Sludge Wave and 80 on Overdrive.

STAB is not enough to make the latter two moves stronger than Boomburst.

252 SpA Choice Specs Punk Rock Toxtricity Boomburst vs. 0 HP / 0 SpD Arceus: 232-273 (60.8 - 71.6%) -- guaranteed 2HKO
252 SpA Choice Specs Toxtricity Sludge Wave vs. 0 HP / 0 SpD Arceus: 181-214 (47.5 - 56.1%) -- 83.2% chance to 2HKO
252 SpA Choice Specs Punk Rock Toxtricity Overdrive vs. 0 HP / 0 SpD Arceus: 199-235 (52.2 - 61.6%) -- guaranteed 2HKO

Sludge Wave is the weakest of the three because it's the only one that isn't boosted by Punk Rock. Boomburst also hits Pokemon that resist Toxtricity's STABs, like Landorus-T and Garchomp.

Here are the differences between the Toxtricity forms.

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I added in the information that Swas said in the comment onto your answer in case someone else might find it useful. Hope you don't mind, Fizz
Sure, but the way it's described is inaccurate. Punk Rock affects Overdrive too; Boomburst is stronger literally because its power is higher.