Slight cases for both characters. Volk is aged down while Zayats is aged up, narrowing the age gap between the two presumably to level the playing field as well as dispel Volk's actions towards Zayats from coming across as a tad predatory.
Biology: Ulya is drawn with horns that resemble a goat's, instead of antlers like a deer's, being female notwithstanding.
The intro is animated in 2D while the rest of the cartoon is 3D. Oddly enough, images inside of a smartphone in this universe become 2D, like when Zayats takes a selfie, the image suddenly switches to a flat drawing.
Smoking and references to alcohol is no longer allowed due to Russian laws prohibiting the depiction of such in 0+ shows.
Badger Tim chastises Volk for this several times in the Ski-Resort Episode, pointing to incredibly specific signs that depict Volk doing something that's not allowed.
In order to appeal to younger kids, the designs are drawn to be cuter and with brighter colors. The usual cartoon violence found in the original has also been toned down, and Volk's long-standing vice of smoking is non-existent, due to Russian laws forbidding smoking and alcohol references in 0+ rated shows.
Gender inverted. Zayats, who is constantly mistaken for a girl by viewers, is redesigned to be less androgynous by making him slightly taller, removing his eyelashes, dressing him in a blue shirt and trousers, and most of all, by giving him a male voice actor after being voiced by females for almost 50 years.
Volk becomes instantly smitten with Ulya, and promptly flirts with her. Despite Ulya being turned-off by his forwardness (and being an overall jerk to her friend Zayats), Volk does not relent on his advances.
Svinka turns out to be one towards Volk, whom the latter ignores. Downplayed in that she's not by any means ugly or a nuisance. Volk just likes to pretend he's above it all.
Ulya is a female roe deer with horns. Does do not have antlers, let alone horns.
Volk. Not that he was a bad-ass to begin with since this is Volk we're talking about, but compare his feats of acrobatics in Episode 4 of the original series to his pathetic display in Episode 3 of this series where, as soon as the steroid-like effects of an apple wears off, can barely lift a barbell overhead. Generally, he's shown to be terrible at sports in this incarnation.