What houses are doing in a chart
Signs describe the sky; houses describe your position under it. The twelve houses map onto areas of life — self and body, resources, siblings and courage, home, children, work and health, partnership, and so on — and where a planet falls among them says which department of life it operates in. Both traditions use twelve houses and broadly similar meanings for them. What they do not share is the method for drawing the dividing lines. Since a chart is cast for a specific time and place, the houses have to be pinned to the local horizon somehow, and there is more than one defensible way to do that. The choice of method is the whole of the difference here.
How whole sign houses work
The Vedic method is the simpler of the two to state. Find the sign rising over the eastern horizon at the birth moment — the lagna, or ascendant. That entire sign, all thirty degrees of it, is the 1st house. The next sign in order is the whole 2nd house, the one after that the whole 3rd, and so on around the circle. Houses and signs coincide exactly, twelve of each, every one thirty degrees wide. Nothing depends on latitude, nothing is squeezed or stretched, and a planet’s house follows directly from its sign. This is also the oldest surviving house system, used in Hellenistic astrology before quadrant methods became dominant in the West.
How quadrant systems work
Placidus, the default in most Western software, belongs to a family of quadrant systems. These fix four points first — the ascendant on the eastern horizon, the descendant opposite, and the midheaven and its opposite point overhead and underfoot — and then subdivide the space between them. Placidus does that subdivision by time, splitting the interval a degree takes to rise. Because the geometry depends on where on Earth you are, the resulting houses are unequal: at high latitudes some become very wide and others very narrow, and near the poles the method breaks down entirely. Koch, Campanus, Regiomontanus and equal house are among the alternatives, each dividing the same space by a different rule.
The practical consequence: your rising sign is your 1st house
Under whole sign, the ascendant does not sit at the cusp of the 1st house with the rest of the sign trailing behind it — the sign it falls in simply is the 1st house, from its 0th degree to its 30th. A planet at 2° of your rising sign is firmly in the 1st house, and so is one at 28°. Under Placidus the same two planets can land in different houses, since the 1st house boundary sits at the ascendant’s exact degree and anything earlier in that sign falls into the 12th. This is the most common source of surprise when someone compares their two charts: not the sign changing, which the zodiac difference already explained, but a planet apparently moving one house along.
Reading a chart in both systems
Neither method can be checked against reality in the way an eclipse prediction can, so there is no experiment that settles which lines are correct. What can be said is that they answer slightly different questions. Whole sign asks which twelfth of the zodiac, counted from the rising sign, a planet occupies. Placidus asks how far a planet has travelled through its portion of the local sky. If you look at your Vedic chart and find a planet in an unfamiliar house, check the house system before assuming an error — this is usually the reason, and it is a difference of convention rather than a mistake in either printout.