I understand your confusion, since particles are ejected from the nucleus in both processes. They’re similar but not the same. Alpha decay may seem to be a bit of a grey zone, since the atom expels a helium nucleus, so the atom is “split” into two very asymmetric parts, but it is generally not considered a fission process. Alpha decay and spontaneous fission are actually competing processes.

And spontaneous fission is possible, but it’s extremely rare. For your example of Uranium, which, in nature, is overwhelmingly (99.3%) U-238:

Spontaneous fission is extraordinarily rare on a per-atom basis. Uranium-238, the most common uranium isotope on Earth, has a spontaneous fission half-life of about 8.4 × 10¹⁵ years.

Source

So with the uranium in your example there is a non-zero chance of spontaneous fission occurring, but it’s very unlikely, with alpha decay being about 2 million times more likely to occur. So, alpha decay will be the overwhelmingly dominant process, leaving virtually no room for spontaneous fission over the short span of a human lifetime.

Beta decay is something else entirely where no protons or neutrons leave the core, so there is no fission to speak of.

EDIT: I see the Lemmy downvote bandwagon has arrived, but I have to ask: