I've always experienced a lot of anxiety. In many ways that was and remains a driving force in my practice. More recently I've experienced more fear. I feel fearful and under threat. They do feel different but I'm still working with them and will be for a long time. In terms of the Buddhist texts and psychology what is the difference between fear and anxiety? Are they spoken about as different things? Are there different Pali/Sankrit terms for them? Is there different ways of working with them?
In traditional Pali, fear is
bhaya-bherava (lit. Fear-Panic), while anxiety is
udhacca-kukucca (lit. Worry-Wrongdoing).
As I understand from the way these are used in suttas,
Fear is defined as an acute sense of danger. It is rather specific, like fear of something coming out of jungle and attacking you. Even if it is uncertain what exactly may happen when you sit in the middle of jungle, fear still has a very clear sense of directionality, there is no expectation that something good may happen, only bad -- otherwise it would not be fear.
Panic is defined as the accompanying sense of helplessness, or sense of our inability to deal with the object of fear.
(More about these two can be found in Dharmafarer's great analysis of Bhaya-Bherava-Sutta.)
While anxiety is defined as either a wavering remorse of something you should or should not have done (
kukucca), or a wavering expectation of remorse you suspect you may experience in the future because you are not doing enough of something you feel you should be doing (
udhacca). So unlike fear, anxiety involves wavering back-and-forth; there is an element of uncertainty in it. Also, the object of anxiety is yourself, your own acts, while the object of fear is external.
As explained by Buddha, the recommended way to deal with fear is by switching focus from obsessive waiting for the object of fear to appear, to getting ready to deal with it should that actually happen. While the recommended way to deal with anxiety is by developing one's wisdom, esp. understanding of Dharma, Three Marks of Existence, and (in Mahayana) by deepening one's realization of Emptiness.
Andrei's answer defined "anxiety" as "remorse" or "expectation of remorse".
Assuming that's so, then the "way to work with it" might be sila i.e. virtue.
The Kimattha Sutta says,
Skillful virtues have freedom from remorse as their purpose, Ananda, and freedom from remorse as their reward.
Or the Cetana Sutta,
For a person endowed with virtue, consummate in virtue, there is no need for an act of will, 'May freedom from remorse arise in me.' It is in the nature of things that freedom from remorse arises in a person endowed with virtue, consummate in virtue.
As a layperson you presumably have a lot of responsibilities towards various people (which is perhaps why some people choose to ordain instead).
Still I suppose the theory is that if you meet those responsibilities then you have nothing to feel remorseful about.
Maybe those suttas are intended for bhikkhus, whose responsibilities (and therefore whose virtues) are a bit different from laypeople's. For example, this introduction to the Vinaya starts by quoting,
Discipline is for the sake of restraint,
restraint for the sake of freedom from remorse,
freedom from remorse for the sake of joy,
Still, maybe something analogous (i.e. practising virtue as an antidote for remorse and anxiety) is true for laypeople also.
Anxiety is also one of the translations of dukkha, so the nature of anxiety (and its cessation) might be fundamental.