However, after doing a little more research, I guess there IS a difference between the stitches and the difference is how they appear on the back of the fabric or canvas. I found this description of them through Wikipedia:
There are three types of tent stitch, all producing the same appearance on the front of the canvas but each worked in a slightly different way and having particular characteristics, uses, benefits and drawbacks. These variants of tent stitch are known as basketweave, continental and half cross tent stitches:
- Basketweave tent stitch
The basketweave form of tent stitch is worked in diagonal rows up and down the canvas. The yarn on the back of the canvas has a typical basketweave Here appearance, with alternating horizontal and vertical stitches. Basketweave is the best stitch to use for covering large areas of canvas as it does not distort the canvas as the other two forms of tent stitch do.
- Continental tent stitch
Continental stitch is worked horizontally or vertically across the canvas. On the back of the work, the stitches appear diagonally across two threads. This method uses more yarn than half cross stitch tent stitch but is more hardwearing.
- Half cross tent stitch
Half cross stitch is worked horizontally or vertically across the canvas. On the back of the work, the stitch appears vertical or horizontal, not diagonal, and crosses only one thread. This method uses less yarn than other stitches but is not very durable as coverage on the back of the canvas is a little thin.
If you are going to be tent stitching a piece, I have found I typically use more strands of floss than in a regular full cross stitch so that you get the fabric coverage. I recommend doing a test patch in a corner of your "border" area or on another small swatch of fabric to see how many strands YOU like best for the count of fabric you're working on.
Here's a close-up picture of a piece I did using the half cross tent stitch using a #12 Kreinik metallic braid on 14-count fabric: