Synthesizers are musical instruments which produce sounds electronically and are often controlled using a piano style keyboard. They often have some sort of sound source (oscillator), some sort of filter and envelope to shape the sound, and an amplifier so that you can hear the sounds they make.
These are all usually made by one company and wrapped in one container. Modular synths on the other hand are…well modular and you use cables to connect individual modules together. Modular synths do not have a keyboard and you can purchase each of the aforementioned components from different manufacturers, but you do need to purchase a case to contain them all. There are a lot of cases out there and they can be quite expensive. They are often not always the ideal size or if you decide you want to buy more modules, you have to buy a larger case. I found an expandable 3D printable case on Instructables (https://www.instructables.com/3D-Printed-Eurorack-Case/). You do need to purchase the STL file here (https://cults3d.com/en/3d-model/gadget/expandable-eurorack-case-blocks), but I am really enjoying my case and thanks to the Design Lab, I now have an expandable case at a fraction of the cost. Thanks!!!