Random identifiers and the index they land in
A version 4 UUID is 122 bits of randomness, which makes it excellent at being unique and actively bad at being ordered. Used as a primary key in a database that stores rows in key order, every insert lands at a random point in the index rather than at the end. The tree fragments, pages split, and the write amplification shows up as a performance problem long after anyone remembers choosing the key type.
A ULID encodes a millisecond timestamp in its leading bits followed by randomness. It is the same 128 bits, it is still practically collision-free, it is still safe to generate on several machines at once, and it sorts chronologically as a plain string. Sorting by ID sorts by creation time, and range queries over a time window become possible without a second index.
What a ULID gives away
The timestamp is readable. Anyone holding a ULID can recover roughly when the record was created, and holding two tells them the gap between them. For an order ID that is usually fine and sometimes useful. For an identifier that is exposed publicly and where creation time is sensitive, it leaks something a random UUID does not.
That is the trade in one sentence: a UUID reveals nothing and sorts badly, a ULID sorts well and reveals when. Pick per column rather than per project. Internal primary keys benefit from ordering; public-facing tokens usually should not carry a clock.
Generated where, and does it matter
Values here come from the cryptographic random number generator in your browser, the same source used for key material, not from a general-purpose pseudo-random function. Nothing is requested from a server and nothing is recorded, so no copy of any identifier you generate exists anywhere but your clipboard.
For test fixtures and schema examples that is merely tidy rather than important. It matters when the identifier is going to be a secret - an invite code, an unguessable URL, a one-time reference - where a value that was transmitted, logged or served from a cache is no longer unguessable.