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The phrase "and distinct types of" is correct and usable in written English.
It can be used when discussing various categories or classifications that are clearly different from one another.
Example: "The study examined various species of birds and distinct types of mammals found in the region."
Alternatives: "and different categories of" or "and separate kinds of".
Exact(11)
In 1974 B.W. Chappell and A.J.R. White discovered two major and distinct types of granitic rock namely, I- and S-type granitoids.
According to a previous study [8], noise type classification accuracy using a Gaussian mixture model (GMM) for four known and distinct types of noise is nearly 100%.
The coincidence of these two separate and distinct types of sensory data contributes evidence to the overall coordination of the spatio-temporal orders of the different sense modalities.
Compared to the Aristotelian conception, Malebranche's conception of causation is remarkably simple and unified, and does not face the question of how such diverse and distinct types of Aristotelian causes can come under a single conception of causation.
However, recent conjectures by astronomers suggest that globular clusters and dwarf spheroidals may not be clearly separate and distinct types of objects.
The human spirit engages in a recursive process entailing four distinct states and distinct types of outcome.
Similar(49)
By using an event-related design and analyzing distinct types of correct and error trials, we aimed to elucidate the role of prefrontal activity in remembering and forgetting.
These differences can make males and females distinct types of hosts, offering different challenges and opportunities to their parasites.
It has recently been demonstrated that the adult dopaminergic system is composed of two functionally and molecularly distinct types of DA neurons with anatomical segregation in the midbrain, and with non-overlaping axonal targets [12].
Studies of the properties and motion of water at depth have shown that strong currents also exist in the deep sea and that distinct types of water travel far from their geographic sources.
And five distinct types of butters?
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com