Sign and house: two different things
A graha's sign and its house are two different things. The sign is the zodiac division it occupies; the house is its position counted from the Lagna.
What it is
In whole-sign houses the sign and the house are linked by a fixed offset from the Lagna sign. A graha in the Lagna sign is in house 1, and the same graha in the next sign is in house 2, whatever its degree.
How it is worked out or read
A difference between sign and house arises only when the Lagna sign is not Mesha. Two grahas in the same sign always share a house in whole-sign houses, which is a property of the system.
Where it appears on this site
The birth chart shows both the sign and the house for each graha.
Two different measures
A graha's sign and its house are two different measures. The sign is one of the twelve divisions of the zodiac that the graha occupies. The house is the position counted from the Lagna in the chart. In whole-sign houses the two are linked by a fixed offset, so that the house number tells you how many signs lie between the Lagna sign and the graha's sign, plus one.
Keeping the two separate prevents a common confusion. A reader who says that a planet is in Karka may be speaking of the sign, while a reader who says it is in the fourth house is speaking of the house. Both can be true of the same planet in the same chart.
A worked contrast
Suppose the Lagna is Simha. Then the first house is Simha, the second Kanya, the third Tula, and so on. A planet in Kanya is in the second house, and a planet in Mesha is in the ninth. A planet at 29 degrees of Kanya and one at 1 degree of Tula are in different houses, because they are in different signs, even though they are only two degrees apart in longitude.
The contrast shows that the house is a sign-based position, not a distance from the Lagna in degrees. This is a feature of the whole-sign method, and it is why the boundaries are always sign boundaries.
When the sign and house agree
Because the house is fixed by the sign relative to the Lagna, a graha in the Lagna sign is always in the first house, and a graha in the sign after the Lagna is always in the second. The two measures therefore agree in a systematic way, and once the Lagna sign is known the house of every graha can be read from its sign alone.
Why the distinction matters
The distinction matters for reading rules that use the sign and rules that use the house. Some rules refer to the sign of a graha, such as its dignity, and others refer to its house, such as the Manglik count. A reader who mixes them will apply the wrong rule. The birth chart shows both measures, so that each rule can be applied to the right one.
Checking a sign and house quickly
A quick check is to count the signs from the Lagna sign to the graha's sign, add one, and compare the answer with the house the table gives. If they agree, the chart is consistent; if not, a counting error is the most likely cause, and it should be found before the reading goes further.