Lesson
White to move. Main line: 1. Bb3 Kd4 2. Ke2 Kc5 3. Kd3 Kb5 4. Kd4 Kc6
The bishops work as a pair on adjacent diagonals. Placed side by side they cut the board in half, and every time they step forward together the half the enemy king lives in gets smaller.
The king is the piece that actually forces matters. The bishops take squares; the king takes the opposition and pushes. Trying to mate with the bishops alone gets nowhere — this is a three-piece technique.
The tablebase gives mate in 31 from here, comfortably inside the fifty-move limit. That is the practical difference from bishop and knight: two bishops need no special corner and leave plenty of margin.
A three-piece technique
The bishops do not mate. They build a barrier, and the king does the pushing — this is the single most common misunderstanding about the ending, and the reason players flail with the bishops while the defending king walks around them.
Placed on adjacent diagonals the pair cuts the board cleanly in two. Every time they step forward together, the half the enemy king is confined to gets smaller, and it never gets larger again.
Any corner will do
Two bishops cover both colours between them, so mate can be delivered in any corner. That is the practical difference from bishop and knight, where the defender has a corner to run to and the whole technique is about preventing it.
The tablebase gives mate in 31 from this position — comfortably inside the fifty-move limit, with room to be imprecise and still win.
What to practise
Set the position up and win it against an engine a few times without notes. The pattern to internalise is the bishops moving as a unit and the king taking the opposition; once those two habits are automatic, the ending takes care of itself.
Then do the same for bishop and knight. Doing them back to back is what makes the difference between the two obvious, and the difference is the whole reason one is easy and the other is not.
The bishops build the wall; the king drives. Trying to mate with the bishops alone gets nowhere.
Keep the bishops on adjacent diagonals so they act as one barrier rather than two pieces.
Two bishops mate in any corner — that freedom is what makes this the easier of the two minor-piece mates.
Source: Syzygy endgame tablebases (via the Lichess tablebase API) — https://tablebase.lichess.ovh/standard