Nothing wrong with a high horse - you get a better view
Can't speak for others, but let me tell you (more or less) how I see those
two options ...
#1 Managed server - you can do what you like with the box but you don't
get root/administrator access unless you're prepared to waive the SLA and
jump into ad-hoc rates for self-harm fixes. Fee is a flat monthly rate
and includes security updates/service packs as applicable. We'll also
install/configure any packages that require the firm but gentle hand of
god.
#2 Self managed - you have god-like status on the server. You manage your
own installs/upgrades. However break it beyond your own means to fix it
and we'll reload/reconfigure the o/s and networking to get you running
again. Fee is ad-hoc hourly rate.
Plenty more differences, but that's the meat.