Half Double Crochet (hdc) and Treble or Triple Crochet (trc)

 All the rest of crochet stitches are variations on stitches you've already learned. The half double crochet (hdc) is a variation on the double crochet. To start a new row, chain 2 and turn.

Yarn over and insert hook in loop of row below.

 Yarn over and pull up a loop (so far just like dc), yarn over and pull through all 3 loops. That's the variation.

 Yarn over and insert hook into next stitch, yarn over and pull up a loop.

 Yarn over and pull through all 3 loops

 At the end of the row, you can see that hdc is shorter and tighter than dc.

 For triple crochet, chain 4 and turn.

 Yarn over twice (3 loops on hook)

 Insert hook in loops of row below and pull up another loop (4 loops on hook)

 Yarn over and pull through 2 loops. (3 loops on hook)

 Yarn over and pull through 2 loops. (2 loops on hook)

 Yarn over and pull through 2 loops.

 Yarn over twice, insert hook in next stitch of row below.

 Yarn over and pull up another loop.

 Yarn over and pull through 2 loops.

 Yarn over and pull through 2 loops.

 Yarn over and pull through 2 loops.

At the end of the row, you can see that trc is taller than hdc or dc. You can also see a slight difference between 'front' and 'back' of the different stitches. On patterns with rows, you'll see both sides. On patterns with rounds (no turning) right side of your work and wrong side of your work makes a difference.

 I just think this side looks 'smoother' and I like it better for the front.

This just looks more like a 'back' to me.