meaning of 想 as "to want" vs "to think/wonder"
The futility of thinking 想 can be fully understood in English.

I am very confused by the character 想。

This is unsurprising because:

想 has multiple distinct meanings: think, feel, miss, imagine, want, wonder, ...; maybe even opine, deduce, conceive, etc., in certain contexts.
Each of these English words have multiple distinct meanings (in English).
想 is ambiguous, and a given usage can often be reasonably translated to multiple distinct words in English.
Likewise, the English equivalents are ambiguous, and can often be reasonably translated to multiple distinct words in Chinese, some of which don't even involve 想, such as 考虑, 怀念, 觉得, 认为, 要求, 决定.

Thus together, if we translate 想 into English, you're looking at 20+ (word,meaning) pairs, only some of which are valid translations of 想 some of the time.  This is further greatly bloated when we include words in Chinese containing the hanzi 想, such as 想法, 想要, 理想, 想到, 想起, 想象, ...
I therefore recommend: forget the idea of getting a clear understanding of 想 directly via English.  You're wasting your time.
But how can I understand 想?

Can you clarify what &quot;想&quot; means by itself?

No.  And I contend that no-one can using English: the words in both Chinese and English are far too imprecise.  At most, you can say that 想 pertains to some thought process, i.e., something is going on in someone's brain.  If you go beyond this, any description of 想 in English is going to be wrong a non-trivial amount of the time (the translation is hugely context dependent).
Translation catalyst: first replace 想 with &quot;something going on in some brain&quot;.
This is the method I use for understanding what 想 means in a given context.  We use &quot;something going on in some brain&quot; as a catalyst:

first, replace 想 with the deliberately vague &quot;something going on in some brain&quot;,

then, once you understand what the rest of the sentence means, infer the most appropriate English word for &quot;something going on in some brain&quot; from the remainder of the sentence.


For example:

我在想你今天会不会来.
I am [something going on in my brain] if you will come today.
version 1: I am wondering if you will come today.
version 2: I am thinking about whether you will come today.
我想知道你今天会不会来.
I [something going on in my brain] to know if you will come today.
version 1: I want to know if you will come today.
version 2: I would like to know if you will come today.
version 3: I yearn to know if you will come today.

This captures the ambiguity: there are multiple correct translations, and one translation might be better than another depending on context.
What's the difference between 想 vs. 想要 vs. 要?
This might not be 100% accurate, but it works for me:

要 implies something is going to happen---there's no thinking (or just minimal thinking) involved.  [This is among other meanings for 要 which are not related to this topic.]

想要 implies a thought, desire, wish, intention, etc. (i.e., something going on in some brain) that something is going to happen.

想 implies it's purely in the mind (i.e., something going on in some brain), and you haven't (yet) taken steps to achieve it (or have taken minimal steps).



我要吃饺子。
version 1: I am going to eat dumplings.
version 2: I want to eat dumplings.

I'm asserting this (i.e., eating dumplings) is going to happen.  Omitting 想 indicates you're not really thinking about it any more (i.e., &quot;something going on in some brain&quot; is not true).
In English, you wouldn't ordinarily declare &quot;I am going to eat dumplings&quot; to a waiter: (a) it's a bit rude, and (b) it's confusing (the waiter might reply &quot;good for you, but what can I get you today?&quot;).  I think it's for these kinds of English-language customs that 要 is translated to &quot;want&quot;.

我想要吃饺子。
version 1: I intend to eat dumplings.
version 2: I would like to eat dumplings.
version 3: I want to eat dumplings.

Basically if I don't change my mind, I'm going to eat dumplings.  But it is possible I might change my mind.  Importantly, there's a mind involved (&quot;something going on in some brain&quot;).
It means something like: I am thinking about and taking steps towards eating dumplings.

我想吃饺子。
version 1: I desire to eat dumplings.
version 2: I wish to eat dumplings.
version 3: I'm thinking of eating dumplings.
version 4: I want to eat dumplings.

Here, it's all &quot;something going on in some brain&quot;.  Whether or not steps have been taken towards eating dumplings is unstated.  Ordinarily, you'd expect that no steps have been taken.