Cooking at, or below, the boil. Is there any impact that the actual boil has?
The usual difference comes because there are foods which have to reach certain temperature to get done. For example, the collagen in beef needs to be held at above 68C to transform. But I don't know of any food for which the turning point occurs between 98 and 100 C. So, in theory, if a recipe calls for boiling food for a prolonged time, you could also cook it at 98 C and nothing too terrible will happen. You might have to wait a little longer. 

In practice, it is quite difficult to hold water at exactly 98 C for a long period of time. So, unless you have a reason to use a temperature controler at this exact temperature, you will just use your stove at a temperature which brings the water to a boil. 

You have to make a difference between boiling and blanching though. Some recipes will direct you to put a small amount of vegetables in a large amount of boiling water and hold them there for a minute or less, or just use the word "blanch". There, you want the vegetable heat-shocked. It will still work at a lower temperature, but you will get the best quality at a roiling boil. Some starches like pasta are also important to mention here, they also profit from a quick heating. In principle, you could change them to another, colder pot after the surface has gelatinized - even 85-ish C will do - but there is no point to such acrobatics, so people boil it until ready. 

There are more cases where the other direction is important, usually because 100 C is too high a temperature. In these cases, you want to simmer your food at 90ish. The only case where the fact of boiling itself is important is in stock. Boiling distributes the protein scum from the meat into the stock, so people don't let it boil if they want a clear stock.