A bowl gouge with any profile can make push cuts, but only fingernail-grind tools can make pull cuts.
Labeled photo of two bowl gouges.

Bowl gouges can be sharpened at any angle (the bevel) and with several profiles, often referred to as the grind. The bevel (colored blue in the photo, above) sits at the lower tip of the tool, while the wings (colored red) extend from the bevel around the flute along the remainder of the grind. 

The bevel angle is measured using the bottom of the flute as 0°. So a 45° bevel slopes back toward the tool handle more than an 80° bevel. The more acute 45° angle cuts more efficiently, creating less tear-out. The steeper 80° bevel allows for rubbing the bevel while reaching deeper into a bowl and moves the tool shaft away from the bowl rim, providing room to maneuver the tool.

When viewed from the side, the profile at the front of a tool with a square grind forms a 90° angle to the bottom of the tool. A fingernail grind has a swept-back profile. Square grinds sharpen easily freehand, while fingernail grinds require a special jig attachment for your grinder to sharpen.

When turning a bowl, you'll use push cuts and pull cuts. A bowl gouge with any profile can make push cuts, but only fingernail-grind tools can make pull cuts. With a pull cut, you pull the tool toward you with both hands while cutting with the sharpened edge of the wing (a scraping cut) (Photo, below, inset). The bevel doesn't contact the wood. Pull cuts prove easier to control and generally provide a less bumpy surface, but may tear out grain.

Photo using 80 degree bowl gouge
A closed flute with the handle lowered, as shown here, makes a finer cut. For more aggressive cuts, open the flute slightly and level the tool handle.

During a push cut, rub the bevel on the workpiece while pushing forward with the handle (Photo, below, inset). The direction the bevel points guides the tool in that direction. Swing the handle to change direction.

Photo using a 45 degree bowl gouge
Make push cuts from the rim to the bottom of the bark line. Cutting against the grain in this fashion prevents tear-out along the bark edge.