Darse cuenta vs. realizar
'Darse cuenta' and 'realizar' are both Spanish expressions that can be translated as 'to realize' in English, but they have distinct uses and connotations.
Darse cuenta
'Darse cuenta' means to become aware of something or to notice something, often suddenly or after not having noticed it before.
Me di cuenta de que había olvidado mi cartera en casa.
(I realized that I had forgotten my wallet at home.)
¿Te das cuenta de lo tarde que es?
(Do you realize how late it is?)
No me di cuenta de que estabas ahí.
(I didn't realize you were there.)
Realizar
'Realizar' primarily means to carry out or accomplish something, but it can also mean to realize in the sense of making something real or bringing it into existence.
Finalmente realicé mi sueño de viajar por Europa.
(I finally realized my dream of traveling through Europe.)
El proyecto se realizará en tres fases.
(The project will be carried out in three phases.)
No pude realizar mis planes debido a la lluvia.
(I couldn't realize my plans due to the rain.)
Summary
While 'darse cuenta' is used for becoming aware or noticing something, 'realizar' is more commonly used for accomplishing or making something real. 'Darse cuenta' is reflexive and relates to personal perception, whereas 'realizar' often involves external actions or achievements. In most cases where English uses 'realize' to mean 'become aware', Spanish would use 'darse cuenta'.