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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

A2
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

B1
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.