Connection types are raw material, not recipes. Browse a few broad families, reveal the examples at your own pace, and invent the next one.
Semantic connections depend mainly on what clues mean. Wordplay connections depend on the clues as written or spoken objects. Mixed connections ask the solver to cross that boundary—for example, finding a synonym and then noticing its spelling.
Difficulty is wonderfully unreliable.
These labels describe a loose tendency, not a rule. Familiarity, clue choice, obscurity, overlap, and the rest of the board can make a simple mechanism difficult—or an elaborate one easy.
Several additions draw on mechanisms found in Eyefyre’s Connections answer archive (spoilers). The new teaching examples are written for this guide; the families and difficulty labels are Fourfold’s interpretation. A change of subject alone does not make a new connection type.