Da eine Menge Fachbegriffe auftauchen, vermute ich, dass eine englische Antwort dem Verständnis besser hilft:
If Staat is used in reference to an area, it always refers to a politically or administratively defined area, while Land may be used to refer to any larger area, that is somehow usefully defined and connected. (Note that both terms may be used for something other than an area: E.g., Staat may refer to the administration as a whole and Hofstaat refers to a royal court. Land may also refer to the contryside or dry land in general.)
- Any sovereign state (e.g., the United States of America, the Federal Republic of Germany, South Korea, the Vatican) is a Staat. In most cases, these areas could also be referred to as Land. However, the usage of Staat emphasizes the political entity, while the usage of Land emphasizes the geographical entity. In some cases, however, a Staat will not be referred to as a Land, especially if it is perceived more as a political construct than a geographical region. Examples would be the Vatican or the both German states during the Division of Germany (I might be mistaken about the latter, since I am too young). Relatedly, two or more states might form a Land, e.g., the two Korean states (which are Staaten) together are the Land Korea (which as not a Staat).
- Some political subdivisions of sovereign countries are referred to as Staat, e.g., a U.S. state is called a Bundestaat (more about this term later) and some German Bundesländer (Bayern, Sachsen and Thüringen) are also referred to as Freistaat (free state) for historical reasons.
- The main political subdivisions of Germany and Austria are called Bundesländer. Also some smaller German political divisions are called Land, e.g., the Emsland.
- Land can be used to refer to some geographical areas, which do not need to be political entities. For example, das Land der Basken (the land of the Basques) will refer to whatever area that is mainly populated by Basques, no matter what the political divisions are, while Baskenland may refer to this but also to the political division of Spain. Das Land meiner Familie (the land of my family) refers to the estate of my family and may be as small as a field.
Bundesstaat has two meanings, which is undoubtedly very confusing. On the one hand, it can be a sovereign country, which is federal (Bund), e.g., the United States. On the other hand, it can be a part of a federal country, e.g., an U.S. state.
The word Stadt (City) is completely distinct from Staat, not only in spelling but also in pronunciation (Stadt has a short vowel, Staat a long one).