The term Lesser Germany (German: Kleindeutschland, in opposition to 'Greater Germany') relates essentially to Germany without Austria. In the 19th century, a part of the Austrian Empire belonged to the German Confederation. In the revolutionary era of 1848-1850, it was discussed whether Austria or a part of Austria could belong to a new German federal state. In 1867-1871, the 'Lesser Germany' became reality: a federal state under leadership of Prussia and without Austria. After that, the term lost its significance because since then 'Germany' is usually identified as this Lesser Germany.
The other term, Greater Germany, remained in use for those who sought to incorporate Austria or the German speaking parts of Austria into Germany. This became a political issue in the aftermath of World War One and then again in 1938-1945. During the cold war, when Germany was divided, a unified Germany was called 'Gesamtdeutschland'.
Since 1815, the German states had belonged to the German Confederation. Its territory was defined essentially after the Holy Roman Empire. Some member states belonged to the confederation only with a part of their territories, such as Prussia and especially Austria. The territory within the confederation was called bundeszugehörig (belonging to the confederation), the other bundesfremd (foreign to the confederation). Only Bundesgebiet (federal territory = territory within the boundaries of the confederation) was protected by the military provisions of the German Confederation.
In March 1848, revolution broke out in Germany and other European countries. The Federal Assembly, the only organ of the German Confederation, elected a National Assembly to work out a constitution for a German federal state. The German National Assembly also installed a provisional head of state (the uncle of the Austrian Emperor) and government. Initially, it was universally accepted that the federal territory of Austria should be a part of the new German state.
During the course of 1848, it became evident that the Austrian government was not willing to live with the consequences of a German federal state. The German National Assembly refused to accept all of Austria, as this would have burdened the new state with the nationality conflicts of Austria. Only the part of Austria that was already federal territory was welcome, even if it included a large ethnic minority (the Czechs). The rest of Austria had to be separate in terms of constitution, government and administration. The Austrian Emperor would be head of state of both parts in a personal union.