Joining on a M-N lookup table vs keyword searching a single column
It is best to store your tags in a separate table because of the many to many relationship. With something like tagging images you can end up with a very large number of comma separated values that would need to be parsed any time you search your database which will lead to massive performance problems as your data grows.

Going that route and searching for a tag or partial tag will require you to parse through multiple strings multiple times. But if all you are doing is displaying the data to be read then comma separation is a fantastic idea and it would be much faster than joining to another table.

Here is great explanation on why, in general, comma separation is not a good practice.

--EDIT

After looking through the githuh link you have posted and the web site, I think Danbooru is doing a combination of two things. If I had to quickly guess, they are keeping the comma separated values of tags to make it easy and fast to view the text upon a mouse hover. They also seem to be inserting the tags into a well structured set of tables. It may be nice to keep that in mind for your practices but I would recommend leaving that out if you can.