Offline vs CoCalc

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Running on your own computer have its advantages, as does using CoCalc. Some of the advantages of the download version of SageMath:

• Most modern computers, including laptops, have more computing power than the basic plan offered by CoCalc. For example, you can do computations in parallel, as much as your computer allows.
• You can work offline. Great in many situations where an internet connection is not available or just slow.
• Like other files that are important to you, you can backup your SageMath files with your preferred backup solution. They are usually very small.
• You can install software packages, with specific versions, as you wish on your computer. The download version of SageMath already contains a lot.

In any case, it might be wise to export your work from CoCalc periodically, so you will have a local backup in case CoCalc will change their terms or is accidentally unavailable.

CoCalc is an online web-service, where you can run various interactive documents and other software online. The main additional feature for you as a personal user is collaboration (real-time sharing of what you currently work on) with collaborators. The whole environment is managed for you, backup of your data being taken care of, etc. For example, this can be useful for teaching a class, because you do not have to deal with the specifics of everyone's own computer.

The key here is, that SageMath is one of the software utilities which are provided. In particular, it is being taken care of testing that it actually works, plenty of optional packages are installed, and there are also many additional python and R packages in the sagemath environment. There is also a special file called "SageMath Worksheet", which is optimized for working with Sage in CoCalc. SageMath itself doesn't support it.

The offline SageMath download version has a couple of differences:

• the computation runs on you own computer, with your own files. so, when your computer has an issue, your files are maybe gone...
• you can't collaborate with someone else in real-time (that's implicitly clear by "offline")
• regarding functionality, out of the box it is the basic setup of sage, without any extras

Therefore, that last point might be crucial to answer your question: there are features in cocalc's sagemath, which aren't there out of the box when you download it. But everything that's there you can install yourself.