What is a Side Seam envelope and how does it differ from a Diagonal Seam envelope?
Most invitation "A"-sized envelopes have side seams. Think A2, A7, etc
Most commercial sized envelopes have diagonal seams. Think #9 regular, #10 regular, etc.
What is the difference?
Side Seam:
The back of the envelope is put together with two vertical glue seams (as opposed to three triangular flaps) which give a more finished look to the envelope.

Diagonal Seam:
Fitting to their name, seams run diagonally across the back. The back of the envelope is put together as three triangular flaps.
