Two schemes meeting on one planet
Classical rulership assigns each sign to a planet, and Cancer is the Moon's. The Chaldean face system is a separate arrangement that runs the seven traditional planets in speed order around all thirty six faces of the zodiac, starting from the first face of Aries and taking no notice of sign boundaries.
Counting through that sequence brings the Moon to the third face of Cancer. There is no design in it, the two schemes simply coincide at this point, as they do at a handful of others. The triplicity scheme does not agree: it gives this face to Pisces and so to Jupiter.
Where the Sun actually is
Checked at noon in every year from 1930 to 2035, the Sun on 14 July fell between roughly twenty one and twenty two and a half degrees of Cancer. That is comfortably inside the third face, which runs from twenty to thirty degrees.
The range holds so tightly because the calendar and the orbit stay in step. Each common year is a quarter of a day short and leaves the Sun about six hours late at any given longitude, and each leap February pulls it back by close to a day, so the two effects largely cancel over the four year cycle.
What tradition makes of the doubling
Older writing treats a face ruled by the same planet as the sign as an intensified version of the sign rather than a modified one, so the closing face of Cancer is described as the most characteristically lunar stretch of it. Where the triplicity scheme is used instead, the same degrees are read through Jupiter and Pisces, and the description softens in a different direction.
Both are inherited readings and this site does not present either as a finding. What can be checked is the position and the rulership tables, and those are stated above so a reader can follow the reasoning rather than take it on trust.
There is a further oddity in the doubling that is easy to miss. The Moon is the fastest moving body the tradition uses, covering around thirteen degrees a day against the Sun's one, so in Cancer the ruler of the sign is also the least stable thing in any chart cast for it. Where a Saturn ruled or Jupiter ruled sign hands everyone born in the same month the same ruling placement, Cancer hands them one that may have moved through half the zodiac between two birthdays a fortnight apart.
The limits of a date
The sign is certain here, since the move into Leo is around eight degrees further on, which is more than a week of solar motion. The face is secure too, with the position several degrees clear of both the twenty and the thirty degree lines.
Nothing beyond the Sun is settled. The Moon as a body, rather than as a ruler, can be in either of two signs on a single 14 July. The ascendant depends on the minute and the latitude of birth. The widget above uses your year, hour and birthplace to give one solar degree and the exact distance to the nearest sign boundary.
The numbers are worth stating. The Moon as a body is one sign, or two if it crosses during the day, out of twelve across different years on this date. The ascendant is all twelve inside twenty four hours, changing about every two hours and moving a degree every four minutes, and it depends on the latitude of the birthplace as well as the clock. Those are the placements that tell two 14 July charts apart, and neither of them is carried by the calendar.
Questions people ask about this
What sign is 14 July?
Cancer, with a wide margin. The Leo ingress falls around 22 July and this date sits roughly eight degrees of solar motion short of it in every year sampled.
Which decan is 14 July in?
The third decan of Cancer, from twenty to thirty degrees, in every year checked at noon. The position is several degrees clear of both edges of that band.
Why is the Moon named twice for this birthday?
Because two separate schemes land on it. The Moon rules Cancer under classical rulership and also falls on this face when the Chaldean sequence is counted from the first face of Aries.
Does the triplicity scheme agree?
No. It assigns the third face of Cancer to Pisces and therefore to Jupiter, so a source using that scheme will name a different ruler for the same degrees.
What is the solar degree on this date?
Between about twenty one and twenty two and a half degrees of Cancer at noon, depending on the year, with the hour shifting it by up to about a degree.
Does a doubled ruler make the sign stronger?
That is how the tradition describes it, and it is worth treating as description. Nothing measurable changes, and the rest of a chart is unaffected by the coincidence.