What is the difference between images alpine/3.10 and alpine/3.10/cloud?

Just above @stgraber said that those /cloud Alpine images have been removed because currently Alpine does not package cloud-init.

There would be an Alpine container image for LXC/LXD as long as the distribution ends up packaging cloud-init.

Currently, the latest stable Alpine 3.11 does not have the cloud-init package, https://pkgs.alpinelinux.org/packages?name=cloud-init&branch=v3.11

The edge Alpine has cloud-init, https://pkgs.alpinelinux.org/packages?name=cloud-init&branch=edge
which means that Alpine 3.12 is likely to have the package.

I suppose you could file a request at https://github.com/lxc/distrobuilder/issues to get a /cloud for Alpine edge.