Both jars are rosin: resin squeezed out of cannabis with heat and pressure. The difference is what sat inside the press bag. Flower rosin is pressed straight from dried, cured buds. Hash rosin is pressed from hash that was separated from the plant first, such as ice-water hash or dry sift.
That one extra step accounts for most of the practical differences. It doesn't rank one jar over the other.
Separate first, then press
In its explainer comparing bubble hash and rosin, press maker Lowtemp Industries describes two different mechanical routes. Bubble hash comes from cold water and gravity: the plant is agitated in ice water until trichome heads break loose, and those heads are collected through micron-rated bags. Rosin comes from heat and pressure. The same piece lists flowers, kief, dry sift and bubble hash as material that can be pressed.
With ice-water hash, the two routes run in sequence: the wash has already pulled the resin heads away from most of the plant before anything is pressed. Dry sift and kief reach the press after dry screening instead. Flower rosin skips the separation step and asks the press to do all the separating at once. Neither route adds a solvent such as butane or ethanol, which is why both sit under the solventless label. For more on hash as a press input, see what hash rosin is.
What the input changes
The practical difference is how much plant comes along. Lowtemp's flower rosin vs hash rosin comparison says flower rosin carries plant lipids, waxes and oils along with the resin, material the separation step has largely left behind before hash goes into the press. That's a press seller's description, not a lab measurement of any particular jar, but it's why the same company recommends different bags, heat and pressure for each input.
Color tends to follow. Lowtemp describes flower rosin as amber to golden and hash rosin as golden to clear, and its bubble hash piece says flower rosin is generally darker, while noting that a golden result is still possible. Treat color as a hint about input, not a grade.
The input also decides whether "live" is possible. According to Lowtemp, flower rosin can only be pressed from dried flower, since fresh or fresh-frozen flower gives "a soupy mess," so flower rosin is never live. Live rosin comes from hash washed from fresh-frozen plants. That fresh-frozen history belongs to a different question, covered in live rosin vs hash rosin.
What it doesn't settle
The input tells you what was pressed. It doesn't tell you the flavor, potency or safety of the jar on the counter, and Lowtemp's conclusion that hash rosin is the stronger commercial product is a judgment about running a product line. For the jar itself, start with how to tell if rosin is good.
Finding the input on a jar
Look for the input words: "flower rosin," "hash rosin," "live hash rosin." A jar that says only "rosin" hasn't told you what was pressed. Some producers spell it out. Nasha's product page sells unpressed hash and temple balls alongside a cold-cure live rosin, which it describes as made from whole-plant fresh-frozen cannabis turned into its own hash, then pressed and cured to a wet badder. That's the hash-first sequence written as a menu. How to read rosin labels covers the rest of the package.