Onebyone

I know of three paperpiecing methods
1. English paper piecing using a template.
2. Foundation piecing, sewing on a base usually not printed pattern on base.
3. Paperpiecing on paper that has a printed numbered pattern to sew fabric on the paper.

There are many variations within each method.

faykilgore

I've only done traditional paper piecing but I use a flat-headed flower pin when I need to pin the fabric together. Some of the long pieces I've had to pin even after the first two pieces have been attached. Glue also works and can be removed by blotting with a wet cloth if you don't want to wash the entire quilt.

joe'smom

quiltsfor, what you described sounds to me like regular paper piecing, with the addition of an acrylic template (which, if I understand correctly, wouldn't be strictly necessary, but eliminates the need to measure the segments of the paper pattern so to see how large you need to cut your fabric pieces?).

Foundation paper piecing is when you sew fabric pieces onto paper in order to stabilize what might otherwise be a stretchy or hard-to-manage block, like a string block. There is no pattern involved; you use a piece of paper that is a bit larger than your unfinished block, sew strings right sides together extending over the edges of the paper, press after each addition as with regular paper piecing, and then remove your paper after trimming the block to size.