I do agree with Sara’s sentiment on focusing on culture/people and the business focus alignment to your area of interest, but I am not sure how I feel about the segmentation. I do agree there is not a hard line, but below is a different approach to how the industry might be segmented (read how folks describe the industry or folks in industry might perceive themselves):
Strategy Consulting Firms: Main focus is to provide high level strategic advice to companies leadership (C-level and Board). They partake in other things, not limited to, but including implementation, operation etc. These companies would include:
Tier 1- which typical refers to MBB
Big 4 - Which refers to the Strategy side of Deloitte (Monitor), KPMG, PWC (Strategy&), EY (Parthenon)
Tier 2- Typical Non Tier 1 or Big 4, could be called "Other Boutiques"- example could be Oliver Wyman, A.T.K, Accenture strategy, Z.S Associate and a host of others.
Management Consulting Firms: Now this includes everything including strategy consulting, IT, Supply Chain, Operations, Finance, Deals or M&A etc. again the companies above mostly offer such services, but the industry has its way of branding MBB as Strategy, Accenture as IT, A.T.K as operation and Big 4 as financial services based. The irony is that they are all management consulting firms that do a bit of everything, so do more than the others do, but you can do strategy work or IT implementation work at most of those firms.
That being said, it is true that MBB gets a lot of strategy projects, but so does Monitor, Strategy& and Accenture Strategy, just like its true Accenture gets a ton of IT projects, but so does MBB and Deloitte. I don’t have exact data to tell you who have what share, but point is you can end up doing what you want at any firm, if they offer/ sell the service you have interest in.
More specific to your question on if they are the same globally, for the companies described above they operate globally, but sometimes with a slight change in focus (read what the business opportunity might be in that region – Houston firms focus on Energy, San Francisco’s would focus on Tech, Middle East- Oil and Gas and maybe Retail etc.)
Obviously there is more to this, but hopefully this is sufficient to get you a sense of the current industry position.