Help with some Latin

What is the difference between “equitas” and “aequalitas” when translated from the English “equality”?

Equitas is a verb. It’s the second person form of equito/equitare.

“Equitas” or “aequitas” (also a noun) would indicate equity, fairness, justice. “Aequalitas” translates to equality or sameness.

Are you sure there actually is a difference?

It may be just the way the Latin is translated into English.
Older English books used the Æ ligature regularly, but it is increasingly becoming obsolete. It’s usually translated as separate letters now. Thus Æsop’s Fables becomes Aesop’s, and Cæsar becomes Caesar.

Just to be clear, from Wikipedia:

With that in mind, the question then becomes about the difference between aequitās and aequālitās. These are synonyms in some of their senses, but as with most synonyms they do not encompass the exact same range of meanings. I suppose you’re mostly interested in how the words differ in terms of our modern political and social concept of equality. According to the OLD (paraphrased):

Noting that the primary meaning comes first, and the rest are tropical (that is, metaphorical) uses of the term, we see that when they used aequitās in a political or social sense it was in comparison to a level surface. The similar use of aequālitās treats the political notion in terms of how evenly something is portioned out.

Okay looks like I need a check on this
Eng: Working to earn equality and respect
Lat: Laborantes mereo aequalitas et respectus

I do want the idea of working hard rather than just working (opero)

Are you asking about vocabulary about the phrase? Everything is in the wrong form except for “et,” and I’m not sure about respectus as a word choice.

Are you looking for a motto, or a stand-alone sentence? I’d probably put “working” in the infinitive here: labōrāre aequālitātī respectuīque.

Since “to” is being used here in the sense of purpose, this seems like a perfect time for ut + subjunctive.

Some notes from Döderlein’s Hand-book of Latin Synonymes:

I think the sense of respect you want is covered by the Latin word honor -ōris m. Equality, as it is understood in the modern usage is not something you earn. It is something that is presumed to be the default condition of all, not something to be earned, though it is often denied, repressed and abrogated. “Man is born free and is everywhere in chains” as Rousseau put it. You might be looking for something more like dignitās.