What is the difference between 'planed square edge' timber and 'planed all round'?
Planed all round means all flat surfaces have been planed.

Planed square edge means you have one edge planed straight and can measure from there. It's one step up from rough sawn.

Timber finish terms for reference


PAR - Planed all round (both edges and sides)
PBS - Planed both sides
PSE - Planed single edge (gives you one straight edge to work from)
Rough Sawn - raw milled stock


Further designations used in wood grading:


S4S - Surfaced four sides
S3S - Surfaced three sides
S2S - Surfaced two sides
S1S - Surfaced one side
Rough


Note that PSE is not necessarily the same as S1S. The board edge (narrowest dimension) is planed straight and true with PSE. For Cedar trim, for example, you have a wide dimension planed smooth.

The Red Oak I used for window trim was S3S, made for nice top and sides, would have been pretty rustic for the rough side to show.