I would say both descriptions are lacking, but the second description of latitude and longitude (i.e., the "new" way) is maybe slightly better than the first (i.e., the "old" way), but the introduction of "horizontal" and "vertical" are problematic and imprecise. Neither description is wrong, but both are missing key elements. The way I would describe them are that latitude and longitude are a spherical coordinate system (i.e., a way of slicing up a spherical shell) allowing you to uniquely define a position on the surface of the sphere with a set of two coordinates. In terms of the orientation of the lines of latitude or longitude, it's more correct (and maybe easier) to consider them with respect to the rotational axis and the equator of the planet. The equator is a line that marks the intersection of the surface of the planet with a plane perpendicular to the rotational axis that goes through the center of the planet. Lines of latitude (other than 0 degrees, i.e., the equator) are the intersection with the surface of the planet of planes that do not go through the center of the planet, but are parallel to the equator. For this reason, lines of latitude are sometimes referred to as "parallels". Line of longitude, or meridians, are the intersection with the surface of the planet of a series of planes that go through both the center of the planet and the axis of rotation. So if you were to cut the sphere along any line of longitude, you would divide the sphere into two equal hemispheres, but if you were to cut the sphere along any line of latitude but the equator, you would divide the sphere in two unequal halves. Then, in relating the coordinates to the lines of latitude and longitude, because we are on a sphere, we measure these in degrees. The angles between lines of longitude are a little easier to visualize since these all intersect at the poles. The angle between lines of latitude are a little more difficult to picture since by definition lines of latitude to not intersect. Here, it's useful to consider a hemispherical slice along a meridian, i.e., we slice the sphere in half perpendicular to the equatorial plane, bisecting the poles. Then, on this hemispherical slice if we draw two radii between any two lines of latitude and the center of the sphere, the angle between those two radii is the angle between the two lines of latitude. The final piece of the puzzle is the origin of the coordinate system. For latitude, this is not arbitrary and it's fixed to the equator, i.e., to define the degree of latitude we measure the angle between the equator and that line of latitude per above. For longitude, it is arbitrary and we have to pick some meridian from which to measure our angles. Once we have a set of lines, ways of measuring angular distance between those lines, and origins for the two sets of lines, we now have all the pieces to define a unique coordinate for any place on the surface of the sphere. More on reddit.com

As you travel horizontally, in an East - West direction, each longitudinal line, perpendicular to your path, is a mile marker (expressed in degrees of the planets circumference). Where any two Latitudinal lines make a round disc, any two longitudinal lines make a slice of planet cake, from pole to pole. Longitudinal lines are also Meridians - markers of the sun's path, time zones, and more generally regions, rather than locations. On a carpentry bench with a ruler attached, the length of a work piece will be determined by a line on that ruler, a measuring line that is perpendicular to the length being measured. 'Long'itudinal lines run North -South because they are a measure of East-West distance at all Latitudes. Longitudinal planes are massive on a global scale; but as your East-West path crosses each Longitude, it's imaginary presence might be just a small sign - A sign whose flat face, turned toward you, is in a perpendicular North-South plane that marks distance along all East-West lines. Likewise, Latitudinal lines running East-West, are measures of distance and location along all the perpendicular lines running North-South. I hope this helps. More on reddit.com

Click the icon next to the lat/Lon field and choose geographic role or whatever it’s called. See if that helps More on reddit.com

Dividing things into sixty is an older way of representing fractional quantities, used before it was mostly replaced by digits after the decimal point. Very early calculations of the value of pi used this system, going past minutes and seconds to thirds, fourths, fifths, etc. Sixty was used because it's convenient, being evenly divisible by many numbers. Navigation techniques developed while minutes and seconds were still common and we've kept them, much as we have for hours of time, because changing is difficult and there's little reason to do so. Navigation sextants are marked out in minutes of arc that correspond to nautical miles on charts and nautical miles is a firmly established unit of measurement for both ships and aircraft. In fact that's why navigation doesn't use seconds of arc, using decimals after minutes, because traditionally nautical miles were divided into ten cables. Astronomers still use seconds of arc; that's where parsecs come from. But nobody uses thirds or smaller divisions any more. More on reddit.com