The Gare du Nord was originally the Paris terminus of the Compagnie des chemins de fer du Nord (see Wikipedia). The Gare de l'Est was originally the Paris terminus of the Compagnie du Chemin de Fer de Paris à Strasbourg, which became the Compagnie des chemins de fer de l'Est (see also Wikipedia).

These companies, with others, were eventually amalgamated into the SNCF in the 1930s, but by that stage there were already two stations with different railway lines going into each.

In general, trains from the Gare du Nord take the Lille line north (to e.g. Picardy, Calais, Brussels, Amsterdam, Cologne and London) and trains from the Gare de l'Est tend take the Strasbourg and Mulhouse lines east (to e.g. Strasbourg, Luxembourg, Frankfurt, Munich, Moscow). However, trains from e.g. Normandy go into Gare Saint-Lazare, and trains from the south-east go into Gare de Lyon.

The following map shows where the lines from each of the Paris stations go. The original is here, by user Wikimedia Commons user Sémhur.

The Gare du Nord was originally the Paris terminus of the Compagnie des chemins de fer du Nord (see Wikipedia). The Gare de l'Est was originally the Paris terminus of the Compagnie du Chemin de Fer de Paris à Strasbourg, which became the Compagnie des chemins de fer de l'Est (see also Wikipedia).

These companies, with others, were eventually amalgamated into the SNCF in the 1930s, but by that stage there were already two stations with different railway lines going into each.

In general, trains from the Gare du Nord take the Lille line north (to e.g. Picardy, Calais, Brussels, Amsterdam, Cologne and London) and trains from the Gare de l'Est tend take the Strasbourg and Mulhouse lines east (to e.g. Strasbourg, Luxembourg, Frankfurt, Munich, Moscow). However, trains from e.g. Normandy go into Gare Saint-Lazare, and trains from the south-east go into Gare de Lyon.

The following map shows where the lines from each of the Paris stations go. The original can be found here, by Wikimedia Commons user Sémhur.