Both approaches will have the similar effect of making that library available to your application.
The HTML approach causes your dependencies to be fetched and executed at run-time by the browser. Much like you'd include imgs on a page, you can include scripts on a page with the source of the script either inline or from another URI. So, let's say you create an HTML page, put a number of script tags around it, and then hit that page in your browser. Your browser will scan the HTML page, identify all script tags and start downloading them. It will also remember in which order the script tags were found, and it will parse and execute them in that order (unless you use async and defer attributes on them).
Ok, so, browser sees HTML page consisting of various elements, including some script tags, download them (probably in parallel), and execute them (sequentially). Now, these scripts may or may not know anything about each other on the page.
Now, let's go to the realm of React and other rich Javascript apps, which depend on various Javascript libraries.
When you do Javascript Module Bundling i.e. import { something } from "package", this will get picked up at compile time by your Javascript compiler, e.g. React via create-react-app when you do npm run build, or Angular's equivalent script, or other compilers such as webpack, etc. These compilers will scan not just a single file, but rather your entire application. They typically start from an entry point, e.g. index.jsx, and then discover the graph of dependencies and recursively go through each file or module that they identify and discover those dependencies and so on and so forth. Once the compiler is done discovering, resolving, building, and bundling your app, you'll typically end up with a single Javascript file (e.g. main.[some hash].js) which is your application AND all dependencies (all those other modules you imported) bundled together in a single file.
So, you see the big distinction is:
HTML scripts are independent resources that are downloaded and processed by the browser at run time.
Javascript modules are discovered at compile time and end up being bundled together with your application code in a single file.
I'm leaving aside concepts such as package splitting and dynamic references, etc. in order to illustrate the larger distinction; you'll end up reading about variations in each approach as you dig further into them.
HTML Script advantages:
They are fetched independently, perhaps from a CDN, may even already be cached in your browser if another website needed them and downloaded them previously. So things like jQuery, loDash, etc. are common packages that may have already been downloaded, and your browser will benefit from its internal cache.
They can be downloaded in parallel; although you can rely on the browser to ensure that they get executed sequentially. So for example if you had your own script that relied on jQuery having already been loaded, all you need to do is to <script src="jquery.min.js" /> first and then <script src="myscript.js"> and that sequence will be respected.
Javascript Module Advantages
Your code may not need the entire jQuery, lodash, or whatever other library that you're referencing. By importing whatever function of your dependencies that you need in your source code, a smart compiler might be able to artfully scalpel only those functions out of the larger library (tree-shake the library), and you'll end up with a smaller overall download payload.
Your entire bundle can be minified, yielding an optimized package.
Your entire bundle will be (/can be) in a single file. One download, and your entire app is loaded and ready to use. No need to worry about downloading various resources from various URLs.
Hybrid Approach is OK
Feel free to use a hybrid solution! If you inspect your compiled React code, you'll see that the create-react-app compiler will inject a <script src="static/js/main.js" /> element at the end of your HTML document. This means that your app can rely on other`s included higher up in your HTML document. So, feel free to load up some libraries in HTML and reference other ones through JS modules. In fact, there are cases that you'd want to do this; for example, including the Google Maps script can be easily done via an HTML script directive, and your React app can still use the GMaps library.