Markup is not same as Margin
Markup as the name indicates is how much the price of a certain item marked up? If the cost to produce a certain item is $100 and if it is being sold for $200, then the price markup is $100. Markup is in relation to the "Cost".
In the above example, the Cost (C) is $100, Selling Price or Revenue (R) is $200. This would give a Profit (P) of $100 i.e., (P = R - C). The Markup percent (M) in relation to Cost (C) would be 100% i.e., (M = P/C * 100)
The Markup percent is not same as Profit margin. Just because the Markup is 100% in the above example, we cannot say there is a 100% profit margin. This is because Profit margin, to be specific Gross Profit Margin (G) is in relation to the "Selling Price". (note: Net profit margin shows net profit after deducting operating and other expenses)
Taking the same example, the Markup percent is 100% but Profit margin is 50% (G = P/R * 100)
Think of it this way. If the selling price of an item is $200, what is the maximum discount you can offer on that item without making a loss? Can you offer 100% discount which would mean you would be giving it away for free? A 100% discount implies, selling a $200 item for $0. In other words, you are making a loss of $100 which is the cost to produce the item.
Clearly, you don't want to be making a loss and so the maximum discount if you'd like to breakeven is by giving up on your profit margin which in the above case is a maximum of 50%. Put differently, you can offer a maximum 50% discount i.e., you can bring down the selling price by half, from $200 to $100 or 50% discount.
Is 100% profit margin possible? Only if the cost to produce an item is $0. Realistically speaking that is not possible. There always is some cost to produce an item in form of time, material or some combination of both.
The closest you can get is some form of 9s i.e, 99.9%, 99.99% etc.
Taking the above example, the $100 item must be sold for $100,000 (with a markup of 99,900%) for a 99.9% profit margin. The same $100 item will have to sell for $1,000,000 (1 Million), a markup of 999,900% to achieve 99.99% gross profit margin.
Below is a quick reference table to see the relation between markup and margin.