A "long, narrow lake in a glacial trough" is a finger lake (D) where terminal moraine acts a dam to hold meltwater from the retreating glacier.
A tarn (A) is a cirque filled with water.
A playa lake (B) is a salty desert lake often dried out with white salt flats.
A kettle lake (C) forms in a hollow left behind by a chunk of ice that slowly melted in an outwash plain.