What is the difference between creating cookies on the server and on the client?
What you are referring to are the 2 ways in which cookies can be directed to be set on the client, which are:
By server:
The Set-cookie response header from the server directs the client to set a cookie on that particular domain. The implementation to actually create and store the cookie lies in the browser. For subsequent requests to the same domain, the browser automatically sets the Cookie request header for each request, thereby letting the server have some state to an otherwise stateless HTTP protocol. The Domain and Path cookie attributes are used by the browser to determine which cookies are to be sent to a server.
The server only receives name=value pairs, and nothing more.
By Client:
One can create a cookie on the browser using document.cookie = cookiename=cookievalue. However, if the server does not intend to respond to any random cookie a user creates, then such a cookie serves no purpose.
Are these called server side cookies and client side cookies?
Cookies always belong to the client. There is no such thing as server side cookie.
Is there a way to create cookies that can only be read on the server or on the client?
Since reading cookie values are upto the server and client, it depends if either one needs to read the cookie at all.
On the client side, by setting the HttpOnly attribute of the cookie, it is possible to prevent scripts ( mostly Javscript ) from reading your cookies , thereby acting as a defence mechanism against Cookie theft through XSS, but sends the cookie to the intended server only.
Therefore, in most of the cases since cookies are used to bring 'state' ( memory of past user events ), creating cookies on client side does not add much value, unless one is aware of the cookies the server uses / responds to.
References: Wikipedia