That's much of it, in PE you might also have high-yield bonds as part of the debt capital structure. Debt people might get involved in structuring so-called 'preference shares' which tend to behave in a bondish fashion but I think that's probably still primarily corporate's wheelhouse.
Note that security won't usually be over the buyer's assets - at least in a PE context security will subsist at a few points in the capital structure and ideally down through the assets of the operating company or group of companies. This last bit can become complicated depending on the jurisdictions in which the assets are located or domiciled in the case of an entire corporate entity. Some part of trainee work on int'l deals can involve coordinating the opinions from counsel in implicated jurisdictions.
In either PE or general corporate M&A I imagine the debt lawyers are also involved in discharging any of the debts currently against the target - in most instances you'll refinance target corporate debt upon acquisition (I believe virtually always in a PE context and would suspect overwhelmingly in other M&A also), including operating debts. This would also involve making sure any security in favour of the old lenders is duly discharged.
