It's very simple. All Russian words have tree genders (he, she, it) so in this case "утро" is a neuter, but "ночь" is a female gender. Depends on gender words spelling different. But it's not simple task to explain how to determine which gender should be applied :)

The second one (good night - доброй ночи) is the Genitive case. That's why there's the й letter.

In nominative: Доброе утро (утро is a neuter noun) Добрый день, добрый вечер (день and вечер are masculine nouns). Добрая ночь (ночь is feminine). In genitive: Доброго утра, доброго дня, доброго вечера, Доброй ночи. Now, I don't know the history of 'good day' (or morning/evening alike) greeting and why it most often comes in nominative. In modern Russian in nominative it sounds like a constatation:"the day is good". As to genitive in "доброй ночи" (or, more common when the pesron is expected to go to bed soon: "спокойной ночи") - it is clear. Russian verbs mening 'to wish [somebody something]' are used with this 'something' in genitive:) Often we omit the verb. So "доброй/спокойной ночи" is understood as a wish: 'have a good/calm night'.

It’s very interesting question for Russian natives too. There are three explanations. 1)When we use Добрый день we mean greeting someone. And we use that in Nominative. Logically we must say Добрая ночь (when greeting someone at night). But the fact is that we say Доброй ночи if farewelling. In other words - Я желаю Вам доброй ночи (I wish you good night). And so we use Genitive (ночи - кого?чего?) 2)The second explanation is that we can’t say which cases (Nominative or Accusative) are used in Добрый день и Доброе утро (because there is no difference between inanimate words of male and neutral gender in Nominative and Accusative - Nominative - день/утро, Accusative - день/утро). In case of ночь - we must choose - Добрая ночь или Добрую ночь (Nominative - добрая ночь кто?что? Accusative добрую ночь кого?что?). The second variant is not used at all. Instead of it we use Genitive - доброй ночи (кого?чего?). Also we can use Genitive - Доброго утра и Доброго дня. 3)We say Добрый день и Доброе утро when day or morning are going. It’s a fact (Это день. Это утро. It is day. It is morning). We say Доброй ночи when night is up, is coming. We wish it. I hope I can explain such a grammatical peculiarity))

all nouns in the Russian language are animated (not only people). Еvery noun has a gender identity. They can be different at the end of words. In most cases, nouns ending in consonants belong to the masculine. Nouns ending in a vowel or soft sing belong feminine. Those that end in the letter "o, e" belong to the neuter. So If there is an adjective with a noun, it has the same gender as the noun. All rules have exceptions. For exp: a day(день) is masculine. Nouns also change on cases.Good morning and good afternoon - a polite greeting (It is a statement of fact.When we talk about the facts we use nominative). When we say "good night" we wish the person a pleasant evening, so it's the noun and adjective will change on cases. To express someone's(thing's) relationship to anything(one) we use Cases