What does deploy mean?
Deploying means taking the software sitting on your computer and putting it somewhere on the internet so that other people can open it. Until something is deployed it exists only for you. After it is deployed it has an address anybody can type.
The word carries more weight than it should, because for a long time deploying was genuinely difficult and involved servers, configuration and a good deal that could go wrong. Most of that has been automated away, but the vocabulary stayed behind and now frightens people who have no reason to hear it.
A change to your code does not reach the internet by itself unless something is arranged to carry it. That is why people end up with a live site that is weeks behind what they have actually built. In Ura the step does not exist: once a project is online, every change reaches its address without anybody asking.
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What is the difference between deploying and publishing?
In Ura they are two separate things on purpose. Deploying puts your site online at its own address. Publishing means adding it to your public maker page so people can see what you have made. You can do either without the other.