Seems to me like a distinction without a difference. If it "could" rain it "can" rain and it "might" rain. Are they used in different contexts? In English "could" is more immediate (it could rain tonight), and "can" more general (it can rain here in Spring). Is it similar in Spanish?
I'm an American, and we use "this night" only in a very specific place, for example, "This night has been really fun so far." and "I wish this night could last forever." This is only when you are referring to your experience of a specific activity at night (e.g. a party). In this case, "night" is not a time of day, but a specific event. You are not talking about the entire night, just the portion when the event took place.
Whereas, "tonight" can be used anywhere, including in the sentences above: "Tonight has been really fun so far." "I wish tonight could last forever."
Also, "It could rain tonight." always uses "tonight", NOT "this night".
It's a bit hard to explain, podría is conditional, which technically translates to "would be able to", which we usually simplify to "could": "yo podría ir mañana"-"I would be able to/could go tomorrow". Pudiera is the imperfect (past) subjunctive which translates to "were able to", which we also simplify to "could", but this tense should technically be used only where the subjunctive is required/in hypothetical situations: "Me alegro que pudieras venier"-"I'm happy that you were able to/could come" or "Si yo pudiera comer pescado, lo comería cada día"-"If I were able to/could eat fish, I would eat it every day".
Here's a link that might help: http://www.spanishdict.com/answers/222610/podria-vs-pudiera
If you were studying es -> en you would be taught that there are 4 rules for translating into the English conditional mood. Scary stuff for the Spanish! See https://www.spanishdict.com/guia/el-condicional-en-ingles/
It gets confusing when you compare them because they are both irregular verbs. Quería (imperfect) verte = I wanted to see you. Or, "I was wanting to see you." Podría (conditional) llover... = It could rain tonight. So in your question you are actually comparing two different conjugations.
Quería (imperfect indicative) Podia (imperfect indicative)
Querría (Conditional) Podría (Conditional) *note the addition of one "r" for both words for the Conditional conjugation.
It really really gets confusing. But somehow when you are in spanish speaking countries you end up learning what conjugation to use when just by what feels right and you never learn all these funny conjugation names and all that. Plus some they don't even use, or rarely.
Quería comes from "querer"...notice there is naturally an 'r' in the root of the verb ("quer"). Whereas podría comes from "poder" (with the root being: "pod"). Ongoing past tense can end in "ía", as in "quería". Conditional future can end in "dría", as in "podría" or "tendría"...these words would be "podía" or "tenía" in the past tense. Maybe it is the natural 'r' in "quería" and the natural 'd' in "podría" that is confusing you. It can be very confusing at first.
According to my Spanish teacher, "podria llover" is an expression of "deseo." In other words, it implies that you hope that it will rain. She thought it would be more likely to be used in the countryside with lots of farms.
Puede llover is the most common expression in Spanish as far as I can tell. It means it might/may/could rain.
English grammar rules define English modal verbs as verbs that have to do with 1) the "mood/intention" of the speaker, and with 2) narrowing "possibilities." The modal verbs "can," "may," "shall," and "will' are used to show the speaker's current intentions. The English modal verbs "could," "should," and "would" are used when speaking about a past time OR a future time. The English modal verbs "ought" and "must" are defective verbs that can be used when speaking about a present, past, or future time.
I CAN/MAY (I am able to) _. That is, the speaker is stating that he has two possible courses of action, which are to either do something or NOT do something. I COULD/MIGHT (be able to) _. That is, the speaker is stating that he has two possible future courses of action, which are to either do something or NOT do something. When COULD and MIGHT are used to describe the past, then the past participle BEEN must also be used.
I SHALL/WILL (I intend to) do _. That is, the speaker is stating his objective/future course, which is to do . I SHOULD/WOULD (I intended to/did) do _. With SHOULD, the speaker is stating his obligation, which is to do . With WOULD, the speaker is either reminiscing about a past action OR indicating a preferred future course of action.
As yoelys4 mentions, words in Spanish can two or more uses. In addition, all languages have synonyms, so often more than one word can mean the same thing in some contexts.
In this sentence, poder doesn't mean ability or capacity. Like the English "could" poder can be used to express possibility.