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"Estandarte" is a noun which is often translated as "standard", and "insignia" is a noun which is often translated as "badge". Learn more about the difference between "estandarte" and "insignia" below.
el estandarte(
ehs
-
tahn
-
dahr
-
teh
)A masculine noun is used with masculine articles and adjectives (e.g., el hombre guapo, el sol amarillo).
1. (emblem)
a. standard 
El estandarte religioso que exhibe esta cofradía en Semana Santa muestra a la Vírgen María.The religious standard that this brotherhood exhibits during Easter shows the Virgin Mary.
b. banner 
Los caballeros mostraron con orgullo sus estandartes en el campo de batallaThe knights proudly showed their banners on the battlefield.
la insignia(
een
-
seeg
-
nyah
)A feminine noun is almost always used with feminine articles and adjectives (e.g., la mujer bonita, la luna llena).
1. (symbol)
a. badge 
La insignia del policía indica que es comisario.The police officer's badge indicates that he is a captain.
b. button  (United States)
Regionalism used in the United States
Muchos de los manifestantes tenían una insignia con el símbolo de la paz.Many protesters wore buttons with the peace symbol.
c. emblem 
En la clase de gimnasia, hay que llevar una camiseta con la insignia de la escuela.In gym class, you have to wear t-shirts bearing the school emblem.
2. (standard)
3. (military)
a. insignia 
El traje del piloto tiene la insignia de la fuerza aérea en el brazo derecho.The pilot's suit had the insignia of the air force on the right arm.