uuid1() is guaranteed to not produce any collisions (under the assumption you do not create too many of them at the same time). I wouldn’t use it if it’s important that there’s no connection between the
uuid and the computer, as the mac address gets used to make it unique across computers.
You can create duplicates by creating more than 214 uuid1 in less than 100ns, but this is not a problem for most use cases.
uuid4() generates, as you said, a random UUID. The chance of a collision is really, really, really small. Small enough, that you shouldn’t worry about it. The problem is, that a bad random-number generator makes it more likely to have collisions.
This excellent answer by Bob Aman sums it up nicely. (I recommend reading the whole answer.)
Frankly, in a single application space without malicious actors, the extinction of all life on earth will occur long before you have a collision, even on a version 4 UUID, even if you’re generating quite a few UUIDs per second.