Go down the road同Go straight on 係唔係一樣?

如果你能夠提供更多的資料, 例如這兩個短語的原文, 對解答你的問題會很有幫助.
簡單來說, go down the road 是「作出某個選擇」或「揀o個條路」. 例如 "If we were to go down the road of increasing governmental interference, laissez-faire will be a thing of the past." 即是「如果我們選擇不斷的增加政府干預, "自由治港"將會成為歷史的陳跡.」
go straight on 是「向前直行」. 例如 "Stand in front of Sogo's main entrance, go straight on and you will reach Jardine's Crescent." 即是「在崇光的正門往前直行, 你便可到達渣甸坊.」 (例子中的 go 亦可改為 walk.)
go straight on 亦可引申指「繼續現時的路向/方向/做法」, 但這種用法比較少用. 所以, 如果你能提供更多資料, 方可給你更貼切的翻譯/解釋.

The main difference is that in the former sentence you have specified the "ROAD ", whereas in the second sentence you indicated only the DIRECTION, e.g.
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- If you go down the road, you'd see the traffic lights.(You are on the ROAD)

- If you go straight on, you'd find room 12 on the left.(You are in a hotel)
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But both sentences can have similar meaning if you are on the ROAD given out directions, e.g.
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- If you go straight on, you'd see the traffic lights. (You are on the ROAD)
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It is not that difficult to understand, o.k.?