definition of structures

The first case you showed

struct str // str is the name of this structure definition
{
int a;
float b;
}; // no variable name so this is a definition only, no space is allocated

is the definition of a structure that can be used anywhere in your program. But as a definition it does not create anything, it just defines some information for the compiler.
In the scond case

struct // no name of this definition, so it is anonymous
{
int a;
float b;
} str; // str is the name of this variable, so this is also a declaration of a variable and space will be allocated.

you have defined the structure, but also declared a variable of that structure, so space will be allocated for it in the program. Note that this is an anonymous structure (it has no structure name) so it cannot be used elsewhere.