This is an interesting question, and the answer is not necessarily cut and dry. These terms are often interchangeable, and both are used to describe planed timber. Both are different to sawn or rough sawn wood.
Firstly, let us look at the meaning and definition of each initialism (we consider them initialism rather than abbreviations or acronyms as we use the first letter of each word in the phrase, but instead of combining the letters to form a new word, you pronounce each letter individually). P-S-E and P-A-R:
PSE this stands for planed square edged or planed square edge. PSE means that the edges are not rounded in any way. PSE has had each edge planed perfectly straight, to a smooth finish.
This would indicate that a piece of timber has at least one planed surface adjacent to another face that is at 90 degrees. Although, often considered that all the faces are planned, and at 90 degrees to each other, it could be that just two adjacent faces are planed only. This is where PAR defines this.
Please note: some may define PSE as planed single edge where only one of the faces are planed and the remaining three (if a four sided section) are sawn.
There is also PBS, 'planed both sides' where two opposing faces are planed and the other two remain sawn.
PAR this stands for 'planed all round'. Planed all round wood is sometimes known as 'planed four sides' or 'dressed all round' (DAR). We understand this to describe all faces of a timber section to be smooth planed. This may or may not be square edged timber as it could be planned all round but with each face at different angles and not necessarily at 90 degrees.
It could be argued that both descriptions are the same but, as mentioned above, the subtle differences could simply be to do with the number of faces that are planed, smooth, and the angles to their corresponding faces.
Planed square edged indicates square faces, typically at 90 degrees, with no rounded edges. Planed all round timber - could still be at 90 degrees but confirms with clarity that all faces are planed.
At Woodubuy - we use both PAR and PSE to help people search and find for planed timber. What we offer is timber that is planed all round (all surfaces are planed smooth) and all are at 90 degrees so square sectioned.
Here are some illustrations showing the differences. You will also note the planed wood that we offer.
All are wood sections showing their 'faces' or surfaces.
Fig 1. This is sawn timber, we offer this solution too, note that none of the faces of the wood are smooth.
Fig 2. Shows planed wood as we offer it from Woodubuy. Planed all round with all edges square. PSE and PAR.
Fig 3. We are referring to this as PSE as well as fig. 2 because this has planed faces that are 'square' or at 90 degrees to each other. Although a sawn face still remains, this could still be considered PSE but not PAR
Fig 4. This is still PAR as is fig. 2 as all faces are still planed. The reason we don't consider this shape to be PSE is because the faces are not at 90 degrees.
Fig 5. This is still planed all round (PAR) but not PSE as the corners are not square they are slightly rounded.
What is CLS in the timber world?
To add another term to the mix, fig 5. is often how CLS looks. CLS means Canadian Lumber Standard and refers to timber that has been planed to standard sizes with, typically, rounded corners. However, it should be noted that many countries now supply 'CLS' type timbers. For example (America - American Lumber Standard (ALS), UK, Sweden, Finland) so the term CLS doesn't always mean the timber has come from Canada.
It is sometimes known as 'planed four sides', 'planed all round' (PAR), or 'dressed all round' (DAR)
Due to planing, CLS sizes are substantially smaller than those of the sawn timber from which they are produced.
The section sizes shown in Figure 5, when the wood is shipped dry at 19% moisture content, are machined from sawn sections, nominally 2 x 3 in (50 x75 mm) and 2 x 4 in (50 x 100 mm) respectively. CLS is supplied in six section sizes, between 38 x 63 mm and 38 x 285 mm.
CLS is typically supplied for the construction industry as carcassing or framing timber and is often produced from a low grade, fast growing, softwood (such as pine). The grade and amount of knots is less important as often it is covered by the fabric/finishes of the building.