I understand that a 'Chair' is a traditional title of a professor in the UK.
Nowadays, what is the difference, if any, between a Chair and a Professor in the UK?
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It is the difference between the role or job and the person who is doing that job.
The person has achieved the status and title of Professor. That person can take the position of the "Chair of Computer Science at the University of Somewhere".
Sometimes a particular Chair will have been endowed or funded at a University and then a Professor is recruited to take that Chair. That person could have moved from another Chair at some other University.
Some of the Chair endowments are quite old, like this example from 1702 in Cambridge: https://www.ch.cam.ac.uk/alumni/new-name-our-oldest-chair
As the other answers demonstrate, this is one of those terms that has a variety of different meanings in academia, depending on institution and context.
Historically, British universities had very few professorial positions; typically a university would have one for each broad field of study. These positions were created within the framework of the university's statutes, and are/were known as Chairs. Each Chair exists independent of any particular individual occupying the position, and the university statutes prescribe the procedure for appointing a new holder if the Chair becomes vacant. Sometimes the Chair is associated with the name of a particular individual or benefactor: hence Oxford has (say) the Regius Professor of Hebrew, established by the king in 1546. Many of the positions created in this way continue to exist, and occasionally new ones are added.
In modern times (particularly since the 1990s) universities have sought to award more people the title of Professor, and it has become a job title within the standard framework of career progression. However, most such jobs are not 'written into' the university's statutes in the same way as the traditional Chairs: when holders leave, the position ceases to exist.
Thus, a hypothetical university might establish two chairs: the [University] Professor of Ancient History, and the [University] Professor of Modern History. They might also hire a number of other historians, and give them the title of Professor - but these jobs would have less prestige than the chairs.
"Professor" is a 'rank' (next up from "Reader" iirc), whereas "Chair" is a specific job-role - they do not mean the same thing.
In smaller fields, there will only be one Professor, who will be said to 'hold the chair'.
In larger fields, there may be more than on person who holds the title of Professor, but only one can be the head, or 'Chair' - have a look at the definition of "Emeritus Professor" for more.
For comparison, think of "Princes" - in the UK, Charles has the rank of Prince, so is known as "Prince Charles", but so is "Prince Andrew". However Charles holds the position of "Prince of Wales" (meaning first-in-line to the throne) which is necessarily unique.
Although my observation of the UK system is only "from afar", at Oxford, Cambridge, Durham, Bristol, Warwick, London, and other serious places, one can look through the faculty list ... and see that (as in other answers) "Professor" is a title, more senior than "Reader", etc. There are also "department chairs", who will almost always have the title of "Professor", and are administrative heads of departments, but this sense of "chair" is quite different from, e.g., "The Savilian Chair in Geometry" (or whatever), within a math dept. The person (almost surely a "Professor") holding the Savilian chair is probably not the head-of-department, although certainly has a very senior position, and perhaps is only answerable to administration outside the math dept.
In fact, this is generally parallel to the U.S., where "the dept chair" is "dept head", and is not necessarily any special honor, but, rather, entails much administrative responsibility. There are also "named chairs", like "University Chair in X"... Confusingly, sometimes there is "University Professor in Math" or similarly. In the latter usage (not uncommon in the U.S.), the usage of "chair" and "professor" have merged.
"Chair" is to "Professor" as "Throne" is to "King"/"Queen".
ETA: the cutesy analogy seems to have proved unpopular. The substantive point of my answer was to express the view that "chair" is synonymous with "professorship". Although I still believe, on balance of probabilities, that to be correct, I'm less sure of it than I was, because I found an oration from a University of Cambridge honorary degree ceremony, which is supplied in both English and Latin, and in which "chair" and "professorship" are rendered as different Latin words ("cathedra" and "proueheret" respectively).