If the offer is rejected and Elon continues to attempt to gain control of the company, that would be an attempt at a hostile takeover.
A more typical way of doing this would be to make a proposal directly to the board first. The fact that Elon did it in public means he's trying to pressure the board (via the shareholders) into taking an action they wouldn't otherwise want to take which makes it hostile.
You could then try for a hostile takeover by buying up as much as you can on the open market and possibly to try to get one or two smaller shareholders to sell their shares to get you more than 51% (and in some cases more than 66% aka a supermajority) to be able to call the shots.
I could offer them $150 a share tomorrow, contingent on financing and would get laughed out of the room.
My point is that the number on the offer is not an objective and singular measure of whether this is a good deal for Twitter. Who is making the offer clearly matters as well to how serious it is.
If you borrow from somewhere else it’s just a buyout.
>> A leveraged buyout (LBO) is one company's acquisition of another company using a significant amount of borrowed money (leverage) to meet the cost of acquisition. The assets of the company being acquired are often used as collateral for the loans, along with the assets of the acquiring company.
Note how the second sentence says that the assets of the purchased company can be part of the arrangement, but the “L” in LBO means the buyer’s borrowing, however they accomplish that.