The rainy summer: الصيف الممطر (ac-cayfu al-mumTir)
The summer is rainy: الصيف ممطر (ac-cayfu mumTir)
Notice that I use "c" instead of "S" or "ss".
In "the rainy summer" we have here one entity composed of a noun (summer) and its aattributive adjective (rainy). In such cases in Arabic, the adjective usually comes (after the noun naturally) following all the attributes of the noun (definition, number, gender). In such compound, we are not really stating anything new but we are simply attaching a character to something, in the same way we say (tall Jack, short Sheila, white hand, black hair...etc).
In "the summer is rainy" we have a full sentence composed of a subject (summer) and a predicate (rainy), connected by the verb to be ("is" in this case). In such sentences we are telling information or a status of something we want to talk about. In Arabic, sentences can be nominal (starting with a noun) or verbal (starting with a verb). The translation above for "the summer is rainy" is nominal of course. In nominal sentences, in Arabic, the subject of the sentence is usually defined with AL (so sentences like A summer is rainy are not possible in Arabic and must be re-formulated). The predicate however, in such sentences, do NOT follow the noun in definition as was the case before. It usually comes indefinite (ممطر instead of الممطر).
Hope that clears it up.