Below are three answers: When should we say which, and what is the "difference" between the two terms.
Let's start with Pressure Altitude. There are lots of more-complex answers in various publications about what pressure altitude is, and many of them are already discussed on this site. A "short and sweet" answer is: Pressure Altitude is simply the "height above a standard reference point at an agreed-upon air pressure measurement".
We use sea level as the reference point, and 1013.25 hectopascals (hPa) as the agreed-upon "standard pressure setting". This atmospheric pressure is the equivalent of 1013.25 millibars, 29.92 inches of mercury, and 14.696 PSI.
Pressure altitude is useful for many things, but one of the most important to aviation is that almost all aircraft performance charts are based on pressure altitude. To a pilot making calculations, such as how much runway length will be needed to land or take off, the pressure altitude is one component of that formula.
For example: we know that Denver International Airport is at an elevation of 5430 feet above sea level. If there is a low pressure system in this area of about 970mb, then the Pressure Altitude for DIA will be at about 6500'. When a high pressure system moves in a few days later, the Pressure Altitude could drop down to around 4500 feet. These different pressure altitudes at the same location could prevent some aircraft operations that might normally be doable.
Summed up: Pressure Altitude is how high above (or sometimes below) sea level the current air pressure "feels", and can have a significant impact on aircraft performance.
Q: When should we say Pressure Altitude?
A: Whenever we need to know what the relative height above sea level is for a given location, so that performance calculations can be made.
Now let's move on to Flight Levels. Flight Levels (FL) are "officially designated" pressure altitudes at or above the official transition altitude (TA). These TA and FL designations are different by country, or even within different terminal areas of the same country. As you noted in your question, a Flight Level is determined by setting your altimeter to QNE and then reading the value on the altimeter. But this reading is only a "Flight Level" when the aircraft is above the TA.
Within the US and Canada, the TA is at 18,000 feet of altitude. If the regional QNH is 1013.25 hPa, then Flight Level One-Eight-Zero (FL180) will be right at 18,000 feet of altitude. FL200 will be right at 20,000 feet of altitude. However, if there is a low pressure system then FL200 could be all the way down at 18,000 feet.
(note: In this low pressure example, aircraft will not be assigned a flight level of FL180 or even FL190, because it would be unsafe - the aircraft would actually be at about 17,000 feet and below the Transition Altitude and interfering with other, possibly non-controlled, aircraft. Therefore, on this low pressure day, it would be said that "the lowest available Flight Level is FL200".)
Q: When should we say Flight Level?
A: Whenever we are talking about aircraft that are flying above the Transition Altitude, and assigned to a specific pressure altitude.
And finally, your 3rd question:
Q: What is the difference between the two?
A: A flight level is always "an officially-designated pressure altitude". But, any given pressure altitude is not necessarily a flight level, and will be used for purposes other than just determining flight levels.
