Here is the technical question to your question
1. Abobe Flash ran on the "Flash Player". This was a plugin, i.e. a third party application that was embedded in your browser.
Many Software Engineers (myself included) hated the Flash player. It was proprietary (meaning that we couldn't control or see how it worked internally). And it was a security risk... when you use the Flash Player, it is easy for websites to drop hidden super-cookies that the end user can control. This allowed websites to track and exchange data about users from website to website.
The Flash Player is still available, but it is obsolete.
2. Adobe provided tools to create and edit Flash animation. These tools (which I suspect you have seen) allow people to draw, and animate visually on their screen. Originally these animations would be packages as SWF files and run on the Flash Player.
3. The Internet has moved on. The most popular way to run applications now is HTML5. This has a number of advantages over the (now obsolete) flash player. It is more secure, more powerful and is a transparent standard.
4. Apparently Adobe Animate is a tool to create animations. I was just reading about it. It's main purpose is to create animations for HTML5. As a side feature, it seems to be able to output animations as "legacy" SWF files.
Whether or not Animate is a later version of Flash builder is a matter of marketing. Animate can create animations in the modern HTML5 format (which is the most important thing). It seems it can also output animations in the now obsolete SWF format.
5. You can write animations in HTML5 without Animate. This is an advantage of using an open format. It may be that Animate is still the best tool for your use, but there are other options including writing them by hand.
I hope that helps.