What is a soft-money research position? I have read the term "soft-money research position" a few times.

E.g. Path of a postdoc.


  Another consideration for interviewees is whether to pursue a
  "soft-money" position. A tenure-track university professor is
  typically paid a nine-month salary to teach one or more courses,
  conduct research and train graduate students. During the summer
  months, the professor can optionally pay his or her salary from grant
  money. In contrast, non-tenure-track research professors often hold
  soft-money positions, which require them to cover 100 percent of their
  salary from research grants, teaching and/or administrative
  responsibilities. Soft-money positions offer the advantage of few
  teaching responsibilities, which frees time for grant writing and
  conducting research, but at the expense of job security, since winning
  grants is a necessity. The Hutchinson Center and some other private
  institutions offer a compromise between these systems, covering up to
  half of a faculty member's salary from institutional funds, so
  research grants only have to cover the remainder.


Advice for stats students on the academic job market gives a clear distinction between soft and hard money:


  Before listing the options I should explain the concept of hard versus
  soft money. Revenue in academia comes from tuition (in public schools
  the state kicks in some extra $), external funding (e.g. NIH grants),
  services (e.g. patient care), and philanthropy (endowment). The money
  that comes from tuition, services, and philanthropy is referred to as
  hard money. Every year roughly the same amount is available and the
  way its split among departments rarely changes. When it does, it’s
  because your chair has either lost or won a long hard-fought zero-sum
  battle. Research money comes from NIH, NSF, DoD, etc.. and one has to
  write grants to raise funding (which pay part or all of your salary).
  These days about 10% of grant applications are funded, so it is
  certainly not guaranteed. Although at the school level the law of
  large numbers kicks in, at the individual level it certainly doesn’t.
  Note that the break down of revenue varies widely from institution to
  institution. Liberal arts colleges are almost 100% hard money while
  research institutes are almost 100% soft money.


I'm still confused regarding the exact definition of a soft-money research position: what is the threshold soft-money : hard-money above which a position is regarded as a soft-money position?

Conversely, what is a hard-money research position? Is it any research position that is not a soft-money research position?
It's actually a little bit more complicated than "soft money" vs. "hard money," but the basic idea is that any scientific position can be categorized on the basis of where the money to support it comes from.

In general, "soft money" refers to positions where the funding source is based on external grants and contracts.  As long as there is a sufficient supply of such money that a person can obtain or that somebody else is willing to devote to their support, they are employed.  If that money dries up, however, the position dries up with it, becoming part time or disappearing entirely.

In contrast, "hard money" positions are not directly project-dependent, but instead are created for a purpose by an organization.  Termination from a hard money position only comes either for cause or due to the organization deciding to remove the position and not shift the person to another position.  They are often more secure (thus the notion of "hard"), but not necessarily.  Tenure-track faculty posts are typically seen as the ultimate in "hard" money: they are ultimately supported by tuition, and even if the students stop signing up for a department, it is typically slow enough that universities tend to prefer to allow departments to age to extinction rather than fire faculty.  A corporate research post is also often "hard money" because it is created by fiat in a company's strategic plan, rather than being dependent on external funds.  It is much less secure, however, because it can be removed by fiat as well.

Where it gets complicated is that various different sorts of "hard" and "soft" positions have different levels of vulnerability.  For example, some "soft" positions are effectively amortized over a large group or include bridge funding, such that they may be nearly as secure as a tenure-track position.

It's a good first-approximation, however, in talking about the challenges of academic fundraising and career management.  The basic rule of thumb is: a PI in a "soft" position needs to raise money to pay their own salary, while a PI in a "hard" position does not.  Thus a "soft" position has a hard time surviving on small grants while a "hard" position merely ends up with few students for a while.