I have a requirement to embed Terms and Condition signature (or check mark approval) into a SPA web app and have some trouble making sense of DocuSign's documentation. I would like the user to receive the signed Terms and Conditions document to their email after signing.
Thanks!
The product is going through some transition that is why you are confused. At the present time (Aug 1st, 2023) some new features are not yet available, so I'll answer these questions based on what exists today, but this answer will not "age well"...
Is Click API or eSignature REST API better for this case?
Right now using Click API and Elastic Signing is the way to go for a simple "Terms and Conditions" type of example. In fact, you don't even need to use the Click API at all if your situation is static, you can create the Elastic Template manually and your front-end up will just show it. I suggest you try this https://developers.docusign.com/docs/click-api/how-to/embed-elastic-templates/ and potentially do just step 5. Steps 1-4 are the Click REST API which you can do too, or not, your decision.
Is it possible to accomplish this all on front end?
To do that you need CORS and at present time you cannot use Click API from the client using CORS, only eSignature REST API. However, you can do what I suggested earlier and not even have to worry about the REST API.