What does 'gutter' refer to in the phrase 'throw money in the gutter'? [migrated]

Below are the images of the definition of gutter on Google, which is a trough on the edge of a roof. However, in the phrase 'throw money in the gutter', I imagine gutter means something related to sewage.

Solution 1:

When something goes into a gutter, it eventually goes down the drain, rendering it irretrievable.

Bye, money!

gutter noun
1a : a trough along the eaves to catch and carry off rainwater
b : a low area (as at the edge of a street) to carry off surface water (as to a sewer)
c : a trough or groove to catch and direct something
_{Source: Merriam-Webster}

It doesn’t much matter what kind of gutter or which drain. However, unless you’re a roof rat, you’re more likely to be engaging a metaphorical street gutter for your “throwdown”:

Solution 2:

Gutter

the edge of a road where rain flows away

In older times, without trash collection and good plumbing, it would be a filthy place full of rubbish.