By managed, it usually means that the server will have patches updated, some basic sysadmin time available to assist with questions on it or if system-related issues arise.
However, the specific definition of "managed" does vary a lot from one provider to another so it is always best to clarify and check on this.
With respect to the initial question, you could of course just buy the servers outright and colo them in a data center.
For instance, you could get a Dual Xeon box with specs like those listed for a cost of $2,500-3,500 depending on where you get it from. And then colo it at a lower effective monthly cost.
Those are definitely high-end boxes that you are listing though so they would likely be in the premium monthly pricing range if offered as a dedicated server. I'd say $300-600/month as a guesstimate.
Of course pricing varies so much for everything in hosting these days, you'd have to really build a spreadsheet almost to get a good sense of what various providers would charge for those.