what are the differences between 要 and 想

In some cases, "要" and "想" can be used interchangeably, especially in spoken language, but the meaning may vary depending on the context.

1. "要" (yào):
Indicates a stronger desire or requirement; implies a sense of urgency or importance; often used to express a need or necessity; can also be used to make requests or give orders.
Examples:
我要喝水 (wǒ yào hē shuǐ) - "I need to drink water"
你要去哪里？ (nǐ yào qù nǎlǐ?) - "Where do you need to go?"
我要你明天来见我 (wǒ yào nǐ míngtiān lái jiàn wǒ) - "I need you to come to see me tomorrow."

2. "想" (xiǎng): indicates a less urgent desire or preference; used to express a want or wish; can also be used to make suggestions or ask for opinions.
Examples:
我想吃冰淇淋 (wǒ xiǎng chī bīngqílín) - "I want to eat ice cream"
你想看电影还是听音乐？ (nǐ xiǎng kàn diànyǐng háishì tīng yīnyuè?) - "Do you want to watch a movie or listen to music?"
我想我们可以明天去旅游 (wǒ xiǎng wǒmen kěyǐ míngtiān qù lǚyóu) - "I suggest that we can go travel tomorrow."

"要" is often used to express a strong desire/intention to do something or is going to do something, depending on the context. It can also be used to indicate a requirement or necessity.
For example:
我要吃晚饭了。(I want to/am going to have dinner now.)
他要去北京学习汉语。(He intends to go/is going to Beijing to study Chinese.)
这个工作要求流利的英语口语。(This job requires fluent spoken English.)

On the other hand, "想" is used to express a milder desire or preference for something. It can also be used to indicate a thought or consideration.
For example:
我想喝咖啡。(I would like to have coffee.)
他想去旅行，但是没有时间。(He wants to travel, but he doesn't have time.)
Hope this helps.

"想"和"要"都是汉语中表示愿望、意愿或需求的词语，但它们在用法和含义上有一些区别。

1. "想" (xiǎng):
"想"表示个人的愿望、想法或意愿。它强调主观上的欲望，表达内心的想法和意愿。
例句：
我想去旅行，探索不同的文化。

2. "要" (yào):
"要"表示对某事的需要、要求或必须。它可能带有一定的客观性，强调基于外在因素的需求。
例句：
我明天要去上班，所以今晚不能出去。

区别：
"想"强调个人内心的愿望或主观意愿，如想去旅行。
"要"强调外在的需求、要求或必要性，如明天必须去上班。

“想”着重表示一种愿望、一种打算。
“要”着重表示做某件事的意志,是一种既定的要求。
如:
(1) 我想买两个面包,一瓶牛奶。
(2) 我要买三个面包，一瓶牛奶。
“想”可受程度副词的修饰，“要”一般不受程度副词的修饰，只受表示意志坚定、决心不变意义的副词，如“非、偏、一定”等的修饰能构成“非要·····不可”的格式，表示坚定不变、不可动摇的决心。如:
(3)她很想吃韩国菜。
(4)她老要吃韩国菜。
(5)她一定要吃韩国菜。
(6)她一定想吃韩国菜

01 From the point of view of expressive meaning

The same: Both can express personal wishes and plans.
Different: the tone of "想" is slightly weaker, it just expresses that the person has this kind of thought and intention, but it is not certain whether he will do it or not.

The tone of "要" is very strong. When using "要", the speaker's tone is very firm. It often expresses a very strong desire, or a decision, determination. Generally speaking, the speaker will eventually do so. For example:
1. I 想买个包. (I have the idea of "buying a bag", but I'm not sure whether to buy it or not.)
2. 我要买个包. (Decided to "buy a bag" and will eventually buy it.)

Let's look at another sentence:
3. 我想帮你，但是我也没有办法. (I have the idea of "helping you", but the concubine can't do it!)
Here "想" cannot be replaced with "要", because if "要" is used, it means that it is decided to "帮你", and there will be no more "没有办法".

02 From the point of view of usage

"想" is mostly used when making a request to others, which is more polite and polite. If "want" is used, it seems a little strong or a little casual.
For example: 老师，我想请您帮个忙。 (It should be polite to the teacher and use "想".)
Another example: 小明，我要请你帮个忙。 (Here, "Xiao Ming" is a friend, and you can speak and ask casually.)

03 means negative

"不想" usually means not having some kind of idea or plan.
"不要" is generally used to dissuade others or forbid doing something, which is equivalent to "别". When the subject is "我", it expresses a strong desire not to do something.
For example:
1.我本来不想去，但是他们一再邀请，我就去了。
2.这样做很不好，你不要再这样做了。
3.你以后别来找我，我不要再见到你！

04 When modified with adverbs of degree

Very/comparatively/somewhat + "think"/"don't want"
Definitely/Non+“要” Never+“Don’t”

- 想: would like to, to think, to think of
想, 要 and 想要 can all mean ‘want’ in some sense, but 想 is the least forceful of the three
- 想 + verb as ‘would like to’
In many cases, it might be better to think of 想 as being more like ‘would like to’ rather than ‘want’. When used for expressing wants, 想 can only be followed by a verb or verb phrase. In other words, 想 only means ‘want’ when it's an auxiliary verb.
If you use 想 directly with a noun, it means something a bit different
EX: 我想去巴黎。(Wǒ xiǎng qù Bālí. I'd like to go to Paris.)
我不想见她。(Wǒ bùxiǎng jiàn tā. I don't want to see her.)
If a speaker wants to be very clear and emphatic in expressing ‘want’, they're more likely to use the much more forceful 要.

Both "要" and "想" can be followed by both nouns and verbs. However, their usage and meaning may differ slightly.
① When they are followed by a verb, "要" indicates a strong demand or requirement. It can be used similarly to "要求" (demand) or "必须" (must). "想" implies a desire or a wish to do something without a strong demand or requirement. It can be translated as "want" or "wish."
For example,
"我要喝咖啡" can be translated as "I need drink coffee" or "I must have coffee" (literally: I want to drink coffee).
"我想喝咖啡" can be translated as "I want to drink coffee" (literally: I think about coffee) or "I would like coffee."

② When they are followed by a noun, "要"'s meaning remains as "need" or "require", "want." For example, you can also say "我要咖啡". (=我要喝咖啡。) But when "想" is followed by a noun, it conveys the meaning of "miss" or "long for." For example,
"我想你" (I miss you)
"我想家了" (I miss home)
"我想我的父母了" (I miss my parents)
However, it is not common to use "想" followed by a noun like "咖啡" (coffee) in the same sense.

Besides, "想" can also mean "think"，
我在想怎么解决这个问题。(I am thinking about how to solve this problem.)
我不知道他在想什么。(I don't know what he is thinking.)

想 and 要 both can express wishes and intentions.
要 is more often used to indicate that an event will certainly happen in the future.

depends on what situations,sometimes both could be same meaning

Thank you both, your helps are awesome! If I am to imprint to my own understanding, 要 is "want, want to" or "need, need to", while 想 is "would like to"