小雨 and 豪雨: weaker rain and a temporarily impassable road
Read 小雨 when rain weakens and 豪雨 when a road becomes impassable for a while. Preserve the slightly brighter sky, temporary result, and action taken in preparation for heavy rain.
Walking in drizzle and rain weakening
小雨（こさめ） means light rain or drizzle. 「小雨が降っていたが、傘を差さずに駅まで歩いた。」（It was drizzling, but I walked to the station without an umbrella.） 降っていた gives the rainy situation, followed by walking to the station without an umbrella.
「午後には雨が小雨に変わり、空が少し明るくなった。」（The rain weakened in the afternoon, and the sky brightened a little.） 小雨に変わり describes the rain changing to light rain. 空が少し明るくなった gives a slightly brighter sky. Weaker rain does not become rain stopping completely.
A temporary effect and preparation
豪雨（ごうう） means torrential rain. 「突然の豪雨で道路が一時通れなくなった。」（Sudden torrential rain made the road impassable for a while.） 突然の marks its suddenness, and 一時 limits the period when the road was impassable. Permanent road closure is not stated.
「豪雨に備えて側溝の落ち葉を取り除いた。」（We cleared leaves from the drains in preparation for heavy rain.） 備えて supplies the preparatory purpose, and 取り除いた reports clearing leaves from the drains. Preparation does not establish the rain actually occurring or create a general response procedure.
Intensity and the degree of the result
小雨 and 豪雨 name rain intensity in these examples. 小雨に変わり and 少し明るくなった connect weakened rain with a slightly brighter sky. 豪雨で and 一時通れなくなった connect heavy rain with a temporary effect.
Walking without an umbrella and clearing leaves are actions in the particular sentences. They do not become instructions everyone should follow, and the examples provide no numerical rainfall thresholds dividing the terms.
Does 「午後には雨が小雨に変わり、空が少し明るくなった。」 mean the rain stopped completely?
Show the answer and why
No. The rain changed to light rain, and the sky brightened a little. Weakening does not establish a complete stop, and the sentence gives no numerical rainfall threshold.