Maybe dictionaries are confusing you. These definitions are what I have found in 한국어기초사전:
For -으려고 하다, -으려 하다, -려고 하다, and -려 하다 (Let's just say -려고 하다 from here), 하다 is an auxiliary verb used to indicate that one is attempting or intends to do an action in the preceding statement.
For -고 싶다, 싶다 is an auxiliary adjective used to indicate that the speaker has an intention or desire to do what the preceding statement describes.
These definitions are incomplete because of the following:
- They mention the speaker for -고 싶다; it actually means that the subject of a declarative sentence that ends with -고 싶다 must be the first person. Interrogative sentences, however, usually require the second person to be the subject. -고 싶어 하다 is used for the second- or third-person subject of a declarative sentence. (There are exceptions, but I will not put them here.)
(나는) 오늘 너를 보고 싶어. (I want to see you today.)
(너는) 오늘 뭐 하고 싶어? (What do you want to do today?)
걔가 나가 놀고 싶어 해. (She/He wants to play outside.)
- -려고 하다 also means to be about to ...
아기가 울려고 한다. (The baby is about to cry.)
건물이 무너지려고 한다. (The building is about to collapse.)
- -고 싶다 shows a desire to do an action; the preceding statement of -려고 하다 relates to something one has decided to do and what one is going to do or try. Therefore, these two sentences are different:
(나는) 너를 보고 싶어. (I want to see you.)
(나는) 너를 보려고 해. (I am going/trying to see you.)
The former shows that the speaker hopes to see "you." Whether it is possible for you to see someone or whether you are on the way to someone's location at the moment, you can say "보고 싶어." For the latter, the speaker made up her/his mind to see "you" and she/he will start (or started) to look for "you." Depending on the situation, the latter sentence could frighten or please the listener. Now, let's look at other sentences:
(나는) 피자 주문하고 싶어. (I want to order pizza.)
(나는) 피자 주문하려고 해. (I am going/about to order pizza.)
The former expresses only what the speaker's desire is. She/he may not do anything about it; she/he may want someone else to order it. The latter indicates that the speaker decided to order pizza and will do it if there is no objection/change to her/his decision.
If it is still too difficult for you to understand the differences, please bring your examples and edit your question.