A woodcut will be printed by letterpress, a relief process, an engraving by an intaglio process. In relief printing the white needs to be cut away; in intaglio it’s the black which is cut away.

The Collation has a useful post telling you what to look for in that old book. The key is to study the detail: this example shows why.

You can engrave a clean sharp intersection between two black lines: it’s much harder to carve out a sharp white angle consistently to make the grid as sharp and regular in a woodcut.

Don’t be confused by the fact that a wood engraving carries the word engraving in its name. A wood engraving is basically just a wood cut executed on the grain end of bit of wood, usually boxwood, rather than on the side. A wood engraving will be printed letterpress just like a woodcut. See Printing methods for video demonstrations of the difference between relief and intaglio printing.