In colloquial Spanish the most commonly used (the only one used) is "frase". To be honest, the only place where I heard "oración" was in Spanish class, back in elementary school. They are both a group of words with a meaning, the difference is that the "oración" has a verb and the "frase" doesn't. But again, this is a difference perceived mostly by language experts.

hola mira, frase y oración tienen un mismo significado, es decir que son sinónimos,pero oración tiene también el significado de rogar, rezar u orar en el sentido religioso

Also, note that another (and more common) meaning for "oración" is "prayer".

well, "frase" is the most used, thats true. No need to be an expert. "Frase" can be considered as a statement grammatically well constructed. ex: "El come patatas". "Oracion" conveys a complete meaning. "el come patatas porque le gustan mucho". I am not using "scientific" language to answer you, just intuitive language. True, the usual term to be heard is "frase", but if you go up a level, this is the explanation. So, i could say: frase: S + V +C; oracion: S+V+C (+ complete meaning). Most probably a language teacher, at secondary school, wont explain that way, but the main idea is this.