Difference between "add column" and "add column" with default

Hi.

What is the technical difference between adding a column to a table
and then apply a "set value = ..." to all columns and adding a column
with a default value = ...?

I have seen that the first duplicates all rows, I had to vacuum and
reindex the whole table. Okay so far, I have expected this. But this
wasn't necessary with the second option, nevertheless, fetching some
rows showed, that the value of the new column was my default value.

So, I'm curious: what happens (not) here?

Thx for the explanation.

cug