In chess, "better" refers to a specific situation in which one player has a very slight advantage over the other player, but the final result is still very much in doubt. With perfect play, a player who is better might be able to "convert" their slight advantage into a victory, but in practice players who are better often lose their advantage with even a single inaccuracy because the advantage is so small.
Chess advantages are typically estimated in terms of the approximate number of pawns the advantage is worth. A player who is better typically has an advantage of around one pawn or less. Conversely, a player who is estimated to be at a disadvantage of around one pawn or less is said to be "worse."
However, a player with an advantage of around two pawns or more is said to be "winning" - they have a significant advantage and would not be likely to lose unless they make several mistakes or a serious blunder.
Because "better" refers to a very specific situation in which one player has a very small, almost meaningless advantage, saying one player is "better" is very often followed by "but..." For example, "Now that they have won a pawn, white is better here, but it is going to be extremely hard to convert this advantage into a victory."