who were the equestrians?

[Epictetus]

I don’t think there is a complete consensus and historians are still arguing. We can figure out some things, though. For one, the knights were generally considered in the aristocratic order along with the patricians. T.J. Cornell points out that horses and aristocrats go together simply because of the money and time necessary for horsemanship. More explicitly, see Cicero in his discussion of the Roman constitution:

There is much advantage in the harmonious succession of ranks and orders and classes, in which the suffrages of the knights and the senators have their due weight.

Cicero, The Republic, IV.2.

Moreover, as far as I can determine there were no knights whatsoever involved in the plebeian successions. They were firmly entrenched with the ruling class and they did serve in the senate.

But yes, some knights were originally plebeians:

…having created a great number of knights from the common mass of the people…

Cicero, The Republic, II, 22.

During the so-called “Closing of the Patriciate” this could be a method of upward class mobility, I presume.

This is confusing, but we have to be careful about thinking of a rigid, unchangeable class structure. Cornell goes on to say:

The important point is that in most cases these distinctions do not coincide, but represent contrasts between different kinds of groups. We are dealing with a pattern of overlapping and intersecting status categories, characteristic of a society that was sufficiently complex for the same person to belong to several different groups at the same time, and in which there was a very large range of possible combinations.

Cornell, Beginnings of Rome