Neither, but closer to the second one.
Laser light is not perfectly concentrated, and it turns out that the laws of physics [do not allow it to be](https://en.wikipedia.org/wiki/Diffraction-limited_system). It’s concentrated enough that it stays the same width over typical human ranges, but even the distance to the Moon is enough to spread it out a lot. For a typical hand laser, it would be spread out over thousands of square miles by the time it got to the Moon. (See [this XKCD](https://what-if.xkcd.com/13/) discussing essentially this exact question!)
But aside from spreading out, and occasionally being absorbed or scattered by the very few particles floating around in space (and there are a fair number), depending on the direction you shone your light, it is very possible that it a big chunk of it would travel for billions of years before encountering anything.
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