País vs. campo
While the English word country can be confusing, the Spanish words país and campo have very distinct meanings. País refers to a nation or a state, while campo refers to the rural countryside, a physical field, or an area of expertise. They are not interchangeable.
País
A1País exclusively refers to a country as a political and geographical entity, such as a nation or a state.
Francia es un país conocido por su gastronomía.
(France is a country known for its gastronomy.)
Mi sueño es viajar a un país de Sudamérica el próximo año.
(My dream is to travel to a South American country next year.)
¿Cuántos habitantes tiene tu país?
(How many inhabitants does your country have?)
Cada país tiene su propia bandera y su himno nacional.
(Each country has its own flag and national anthem.)
La economía de ese país depende del turismo.
(That country's economy depends on tourism.)
Campo
A2Campo has several meanings. It most commonly refers to the countryside or rural areas, in opposition to the city. It can also mean a physical field for agriculture or sports, or a metaphorical field of knowledge or activity.
Prefiero la tranquilidad del campo a el ruido de la ciudad.
(I prefer the tranquility of the countryside to the noise of the city.)
Los niños corrían libremente por el campo verde.
(The children were running freely through the green field.)
El agricultor plantó trigo en su campo este año.
(The farmer planted wheat in his field this year.)
Los jugadores ya están en el campo de juego.
(The players are already on the playing field.)
Ella es una experta reconocida en el campo de la biología molecular.
(She is a renowned expert in the field of molecular biology.)
Hay mucho campo para la innovación en esta industria.
(There is a lot of room (field) for innovation in this industry.)
Summary
In essence, use país when talking about a nation (like Spain, Japan, or Brazil). Use campo when referring to the countryside (the opposite of the city), a plot of land (a soccer field or a corn field), or an area of study (the field of physics). You are born in a país, but you might go for a walk in the campo.