I think this is a good question. I experience at least a low-grade level of anxiety pretty-much 24 / 7. But I occasionally experience more severe cases as well. (Perhaps the latter could also be termed "agitation"?) I do think there can, at least sometimes, be a difference in how the two states are handled.

With agitation, while the long-range techniques may be the same as they are for mild anxiety, in the moment what is sometimes necessary (at least for me) is to do something physical. Many years ago, one of my go-to techniques for burning off agitation was chopping wood! But I suppose working out at a gym or perhaps running or swimming laps... something physical such as that... could provide a similar release.

Here are links to 4 articles, from PsychCentral's archives. The first 3 offer tips on how to manage anxiety. The fourth discusses agitation. The recommended techniques are essentially the same:

9 Ways to Reduce Anxiety Right Here, Right Now

15 Small Steps You Can Take Today to Improve Anxiety Symptoms

Top 10 Lesser-Known Self-Help Strategies for Anxiety

What is Agitation? | From the Desk to the Couch