Operators to get a string or more json in Postgres

There are two operators in Postgres that I have trouble telling apart. The -> operator and the ->> operator. They both take a json object on the left and a key on the right, but result in different types.

Given json in postgres that looks like this:

> select '{"a": {"b": 2}}'::jsonb;
{"a": {"b": 2 }}

I can traverse the data structure with the -> operator because it returns a data structure.

> select '{"a": {"b": 2}}'::jsonb  -> 'a' -> 'b';
2

I can get a value as a string from the json with the ->> operator.

> select '{"a": {"b": 2}}'::jsonb ->> 'a';
{"b": 2 } -- ITS A STRING

But if you use the ->> operator to get a string, then you can't traverse the data structure with the -> operator anymore.

> select '{"a": {"b": 2}}'::jsonb ->> 'a' -> 'b';
ERROR:  operator does not exist: text -> unkown