Colonels, captains, commanders and commodores

Paul B. and Len had a discussion earlier in the week on military rankings, and what-compared-to-what between the army and the navy, etc.

Paul found the answers here, for the US services, at least:
http://www.easternct.edu/personal/faculty/pocock/ranks.htm

I'm not sure I understand the difference between commissioned officers (lieutenants, captains, majors, generals, etc.), and non-commissioned officers (corporals and sergeants).
But, all the rankings are there lined up, so that one can see Lieutenant Colonel in the army is equivalent to a navy Commander, and 'outranks' a navy Lieutenant Commander.

So here's a follow-up question: Do ranks apply across services (ie., can a navy Captain order around an army Major?)