In Danish there really isn't that much of a difference. Not if you stick closely to the wording.
"To want" and "want to have" are both covered by "vil have". "Would like to have" would be "vil gerne have"
That said, all this can be expressed differently.
If "want" is meant like "wish for" you can use "ønsker". But it can sound stilted and formal depending on the situation.
"Jeg ønsker mig en karriere i militæret." - I want (wish for) a career in the military.
"Jeg ønsker at have en karriere." - I want (wish) to have a career.) To me this sounds stilted.
It could also be "at kunne tænke sig" (no easy direct translation, but means something like "to think yourself into the situation of doing/having").
"Jeg kunne godt tænke mig en karriere." I would like a career.
"Jeg kunne godt tænke mig at have en karriere." I would like to have a career.
If we ask someone for what they would like we often use this as well.
"Kunne/kan du tænke dig at se en film?" Would you like to watch a movie?
"Kunne/kan du tænke dig nogle popkorn også?" Would you like some popcorn as well?
In a formal setting a waiter could use both of the above instead of "vil have"
"Ønsker De et glas vand." Would you like a glass of water? "Kunne De tænke Dem et glas vand?" Would you like a glass of water?