Where did you find these expressions? The WIKI is open for anybody, it may be that not all is named consistently.
Fabrik is working on databases, with database tables and columns, so it must reference it somehow.
In the element listing you can see
Name: is the "short" element name (feld), which is the column name in the database table
Label: is any label you can give to your element (feld qr code) and you can change is at any time without changing anything in the Fabrik structure
Full Element Name: is a combination of the database table (stadt) + 3 underscores + the short element name, this is e.g. used in placeholders, in examples you'll see something like {tablename___xxx} or {your-table___your-element} etc.
- full_name.name
- fullname.Label
doesn't make much sense.
The [dot] syntax is usually MySQL syntax if you (as an experienced user) are using SQL statements directly (e.g. if you want to display a "concat" label of a databasejoin element or adding a (SQL) WHERE condition to filter databasejoin options.
Fabrik has a lot of hooks to do additional MySQL, php, JS but if you use them you must know what you are doing.