A server has fewer power concerns, and is all about throughput. Heat, size, are not as relevant (but not irrelevant).
iPhone and iPad are obviously clients. A Mac Pro is a Server. A macbook air is probably a client (though, ironically, it is far more powerful than the $10K servers I had in 1999). A MacBook Pro falls somewhat in the middle, but leans towards client. An iMac is also in the middle, but leans towards server.
I think the angst (which I have to some degree as well) about the distinction between Client vs Server, is because it's not completely clear how to position the Mac Pro and iMac. In some benchmarks, the iMac meets, or exceeds the MacPro. But, in terms of sheer throughput for bulk tasks (Video Rendering), you can get a higher top-line performance from the MacPro. And, for day-day interaction, the 5K Display of the iMac (human-computer interaction), beats out the MacPro.
[edit: 99.99% of the time, downvotes are immaterial to me, but I'm genuinely intrigued in what the contrary opinion is here - I expect to learn something, please share!]