There is no shame in learning to snowboard. I know that may sound counterintuitive after a day of tumbling down a mountain on your face while hundreds of tittering pre-teens go zipping by, but I assure you, the vast majority of folks staring from the chairlift will understand. The most important thing for saving face at this stage is to not get overzealous with the lingo. A good place to start would be to understand the term carving before ever attempting to use it.
Carving is a state of snowboarding where the board is always traveling parallel to its edge. This means the edge is not sliding at all as you move. It's just like ice skating. It leaves a smooth and deep line through the snow. Alpine boards are made to carve, with a deep sidecut and long edges. Freestyle boards will be harder to carve with, but it's still possible, especially if the edges are sharp.
How to Carve on a Snowboard
Carving is not very hard, but it does require a fair amount of board control and some balance. When you see a beginner snowboarder (or skier), the obvious giveaway is that they don't keep their board pointed very straight, it kind of wobbles around as the go. This is largely a matter of muscle knowledge, after a few days your muscles will catch up and keep the board pointed in some direction.
Why is board control so important? Because carving is essentially holding the line between a controlled skid (aka. slowing down gracefully) and catching an edge (aka. faceplanting). The first thing you learn in snowboarding is not let your "downhill" edge dig in, because you will flip. So the natural response is to keep as far away from the wrong edge as possible. This is why when beginners first link turns, they will struggle to transition between edges, and will whip the tail end around dramatically with each turn. All this is fine for learning, but it will severely hamper your snowboarding development in the long term.
The insight to carving is simple. Snowboarding does not require any twisting motions whatsoever. If you are standing straight, with your board pointed down the hill (you are facing the side of the run), leaning onto your toes will perform a toe-edge turn, and rocking back onto your heels will perform a heel-edge turn. If your edges are sharp enough and the snow is hard enough to hold your momentum, you will carve a glorious arc through the snow.
Once your edge is locked into the snow it will provide some resistance against twisting forces, so suddenly catching an edge will not be much of a danger despite the opposing edge's rotational proximity. The semi-dangerous moment will be when you are transitioning from heel to toe or vice versa. At this precise point your board will be traveling forward on neither edge (*gasp*), but don't panic! As long as you don't twist your board you can't catch an edge. You can lean forward or backward at this point to turn either way smoothly. In fact, expert carvers often do both. They transition their front foot before their back foot so for a instant both edges are actuated by twisting the board lengthwise (like taffy).
To develop your carving technique I recommend focusing on body position. Keep your body in a neutral position, and rotate only your head to look down the hill. There will always be a little rotation going on to maintain control, but keep it to a minimum, and instead focus on leaning to make turns. Once you've mastered the art of carving you can learn it all over again riding fakie! Good luck!