Let's look at the specific examples:
$ nslookup u-psud.fr
So, u-psud.fr -> 188.8.131.52
$ nslookup www.u-psud.fr
www.u-psud.fr canonical name = cms10-default.u-psud.fr.
And, www.u-psud.fr -> 184.108.40.206
So, in short, you are connecting to two different web servers.
The history of this is more convoluted. A long time ago, as the Internet grew in popularity, many of the services you know were only growing in popularity. Most of the users were local, so systems often appeared as what they were named locally. (I saw a list circa 1990 that showed the most popular hostnames were things like:
When the Internet usage became more globalized, smart administrators started naming their SMTP hosts "mail", their POP servers "pop" and their FTP servers "ftp". (You would be amazed how hard it was to convince people this made sense...)
For a long time, DNS-smart-but-lazy administrators tried to serve everything off a server for the top level entry (domain.com). These days, few administrators are this foolhardy, you need to spread out the load across several systems. From a naming perspective, using the name-of-service-in-the-domainname makes a lot of sense for end users, it is hard to get wrong.