The lines that intercept latitude lines are lines of longitude.
The latitude lines printed on a map will depend on the scale of the map. A map of the Earth will probably have latitude lines printed every 15 or 30 degrees; a map of the United States will have latitude lines printed every 5 or 10 degrees.
On a map, longitude lines go up and down, AKA vertically. Latitude lines are horizontal lines on a map.
longitude
Parallel lines found on a map correspond to latitude.
The lines that are perpendicular to the latitude lines on a map are called longitudinal lines. There are 24 of them, each representing 15 degrees of change.
There can be various lines on a map, but the ones you are probably thinking of are 'latitude' and 'longitude'.
Most maps will show latitude and longitude lines, if not, they're ALWAYS on a globe.
grid lines of longitude and latitude
They are the horizontal lines on a map.
Not all maps show latitude and longitude. On those that do some have horizontal lines indicating where lines of latitude lie, and on the right and left margins of the map these lines will have the latitude they represent marked. Then on some maps the lines are missing but the notations in the margin show where the lined of latitude should be.
Latitude and longitude
The lines on a map or globe that go vertically and match with the lines of latitude to tell the exact pin points of a place.