不断 + [verb]
不停(地) + [verb]
[verb] + 个不停
[noun] + 不断
不断 and 不停 both go before a verb and say an action keeps going. 不断 describes a process that develops over a longer stretch – improving, growing, changing – and may move in steps. 不停 describes one action carrying on without a pause.
Verbs of growth and change – 提高, 发展, 增加, 进步, 变化, 学习 – go with 不断, which is neutral to written. With 不停 they sound as if the change were happening minute by minute.
Physical, audible actions – talking, crying, raining, ringing, pacing – go with 不停, the everyday spoken word. 地 often follows it. Only 不停 fits the frame verb + 个不停, "won't stop …".
不断 can also stand after a noun as the whole predicate: the thing keeps coming. 掌声不断 is "the applause went on and on", 问题不断 "one problem after another".