They're all the same kind of thing — a ratio
Percent, ppm, ppb, and ppt all express the same idea: a part relative to a whole, as a dimensionless fraction. Percent means "per hundred" (÷100). Ppm means "per million" (÷1,000,000). Ppb means "per billion" (÷1,000,000,000). Ppt means "per trillion" (÷1,000,000,000,000). They're the exact same kind of ratio, just written with progressively larger denominators — useful because percentages become awkward to read once a concentration gets extremely small (0.0001% is much less readable than 1 ppm).
The exact conversion factors
1% equals exactly 10,000 ppm (since 1/100 = 10,000/1,000,000). Working the other direction: 500 ppm equals exactly 0.05%, and separately equals 500,000 ppb — each step down in unit size multiplies the number by 1,000, since each unit represents a denominator 1,000 times larger than the one before it (million → billion → trillion).
Why water-quality contexts use mg/L almost interchangeably with ppm
For a dilute aqueous solution — water is the overwhelmingly common case — 1 ppm by mass works out to very close to 1 milligram of substance per liter of water (mg/L), because water's density is almost exactly 1,000 grams per liter. This is why water-quality reports (drinking water standards, pollutant limits) commonly state a ppm concentration alongside its mg/L equivalent: 500 ppm and 500 mg/L describe essentially the same concentration in water specifically. This mg/L approximation holds for water; it isn't a universal equivalence for ppm in other substances or solvents with different densities.
A worked example — a common water-quality figure
A total dissolved solids (TDS) reading of 500 ppm in drinking water corresponds to about 500 mg/L — a figure often cited near common acceptable-taste thresholds for tap water. The same 500 ppm also equals 500,000 ppb, which sounds far more alarming as a raw number despite describing the exact identical concentration — a good illustration of why picking an appropriately sized unit (ppm here, not ppb) matters for how a figure reads, even though the underlying quantity hasn't changed at all.
When each unit size is typically used
Percent suits concentrations in the rough 1-100% range. Ppm suits much smaller concentrations common in water quality, air pollution, and chemical trace analysis (typically single digits to low thousands of ppm). Ppb and ppt are reserved for even smaller trace concentrations, common in environmental toxicology and ultra-pure material specifications, where a full ppm figure would need many leading zeros to express.