The phrase "a further distinction between" is correct and usable in written English.
You can use it when you want to elaborate on differences or categories within a specific context or subject matter.
Example: "In our analysis, we will make a further distinction between qualitative and quantitative research methods."
Alternatives: "an additional differentiation between" or "a more detailed distinction between".
A further distinction between the two is in the number of flower parts.
A further distinction between scale and raga is found in the varying emphasis placed on different notes in a raga.
There is a further distinction between what is called book hand and the business, or court, hand at one time used for documents.
Within sets of elementary structures (or positive rules), Lévi-Strauss made a further distinction between systems of "restricted exchange" and those of "generalized exchange".
A further distinction between singing and speaking is the control that is required, in singing, of the movement and reflexes of the larynx.
There is a further distinction between setting up a shell company in a low-tax jurisdiction and buying a swanky flat with three shell companies, with the purchaser's name replaced on the paperwork by a bunch of fake directors.
While such explanation might work well for the use an individual speaker learns to make of the expressions of an existing language, whether any distinction between rule explained and merely regular behavior has been substantiated now depends on substantiating a further distinction: that between a system of rules and one of mere regularities.
This last finding points to a further distinction, that between observing the actions of another and imitating those actions.
Sometimes a further distinction is made between Deutero-Isaiah (chapters 40 55) and Trito-Isaiah (chapters 56 66).
A further distinction is made between the peoples of the plateau and those of the coast.
For non-robust invariants, a further distinction is made between processes that directly transfer some quantity from large to small scales, and processes involving a cascade through a continuous range of scales; such cascades may either be explicitly parameterized, or handled implicitly by the dynamical core numerics, accepting the implied non-conservation.
