Postgres has three kinds of integers. Or rather three sizes of integers.
There are smallint (int2), integer (int4), and bigint (int8)
integers. As you might expect, they are 2 byte, 4 byte, and 8 byte integers
respectively. They are also signed integers. All of this has implications
for what ranges of integers can be represented by each type.
The smallint integers have 2 bytes to use, so they can be used to
represent integers from -32768 to +32767.
The integer integers have 4 bytes to use, so they can be used to represent
integers from -2147483648 to +2147483647.
The bigint integers have 8 bytes to use, so they can be used to represent
integers from -9223372036854775808 to +9223372036854775807.
Though columns can be restricted to use a particular-sized integer, postgres
is smart enough to default to integer and only use bigint as necessary
when working with integers on the fly.
> select pg_typeof(55);
pg_typeof
-----------
integer
> select pg_typeof(99999999999999999);
pg_typeof
-----------
bigint