What they share
The planetary attribution, and with it a whole set of associations: colours, days, gemstones, remedies, temperaments. When Indian numerology says a Mulank 8 is tested early and rewarded late, it is describing Saturn, and a jyotishi reading a Saturn-dominant chart would say something recognisably similar.
The compatibility scoring on this site is the clearest case. It uses the classical planetary friendship table from jyotish, applied to the planets that rule two people's numbers — the numerology is the input, the astrology is the mechanism.
What they do not share
Jyotish is astronomical. A kundali is computed from where the planets actually were at a specific moment and place, which is why it needs a birth time and a city, and why it can be wrong if the time is wrong.
Numerology needs neither. It works from a date and a name, using arithmetic that would give the same answer on any planet. This makes it far more accessible and considerably less specific — a numerology reading applies to everyone born on the same date, a kundali does not.
Which to use for what
Use numerology when you have a date and no birth time, when the question is about a name or a business, or when you want a quick frame rather than a detailed one. It is the right resolution for 'what is this year about' and for 'does this brand name fit this business'.
Use jyotish when the question genuinely needs specificity: matchmaking, dasha timing, doshas, remedies prescribed for an actual chart. A gemstone in particular should never be chosen from a number — it is prescribed from a chart, and wearing the wrong stone is the one place this distinction has a practical cost.
The honest summary
They are two traditions that borrowed a vocabulary from each other, and the borrowing runs mostly one way — numerology took the planets. Neither validates the other, and a page that presents numerology as 'the mathematics behind astrology' is making a claim neither tradition supports.