Well, traditionally, serif typefaces have a lowercase t that is "spiked", and so sans-serif faces may, to a varying extent, preserve some of the traditional features of serif typefaces.

It is a reference to the the stroke made with a broad-nibbed pen.

And the cut makes its shape more unique, i. e. more distinguishable.
Best example is Univers, where all terminals are cut either horizontally or vertically.

Which do you prefer? Does your answer depend on what the rest of the font looks like?

The shape of "f" has some bearing on the matter.

So you can tell apart Arial from Helvetica ;-)

Is it correct to say that the slanted is termed grotesque and the flat terminal neo-grotesque (or am I oversimplifying)?

Is it correct to say that the slanted is termed grotesque and the flat terminal neo-grotesque…

Neo-grotesque does not describe the actual style of a typeface—just what style of graphic design certain types have a tenuous historical connection to.

Oh, rebellious lowercase t. Why can't you be like Endicott?

@Nick Shinn

The shape of "f" has some bearing on the matter.

Can you please explain that more?

The slant is one of the ways we can differentiate between i j t l f r and the like. Think of its use (or lack there of) as part of a larger system that must sensibly create glyphs appearing as a family, adjoining harmoniously with neighbors, yet retaining a sufficient self image to not be confused with a cousin. With sans serif, the historic slant of the pen is less important than shapes that fit and play nice together. It isn't a case of either always or never use the slant but a case of use it well and sensibly when you do.

f and t design one another. When designing a font, there's always some back and forth play between which affects both forms. Lots of letters affect one another but ft and gy are special pairs with powerful relationships. Heavy, man.