OK, remember a few things about Lucas' favorite droids:

They are possibly not sentient. Sentience in Star Wars seem to be a fine line, and to be completely honest - does not seem to be consistently defined (it seems confused with free will), however the linked answer seems to rely on them not being slaves because they are not sentient. If they were sentient, it would explain a lot being asked here. They do not appear to be particularly high end or expensive models. In fact, depending on what level of continuity you follow they seem to be found or sold out of junkyards repeatedly (especially Threepio). They seem to both have after market upgrades though. C-3PO's trademark color was granted as part of his service to Amidala, IIRC. Many of R2's more .. ahem ... specialized functions are listed as aftermarket upgrades for R2 units in the Wookieepedia, although who installed them is left a bit of a mystery... Chronologically it would have to be an unnamed mechanic on Naboo who is probably the most undervalued person in the galaxy.

Or in short: they aren't special. In fact they are rather old. And cheap. They'd just been hot-rodded a little. They are the Star Wars equivalent of your friend's Trans Am. However their behavior, and the behavior of those around them, is a bit odd for a pair of off-the-shelf droids:

C-3PO often expresses opinions and even emotions (particularly fear, but also joy).

R2 express emotion as well, he just does it indirectly or via proxy (C-3PO notes his "relief" in ESB)

Those first two I note because emotions are odd for non-sentient beings...

R2-D2 is an astromech droid who spends the vast majority of the films not fixing ships

In fact, R2 is probably the most accomplished slicer we see in action, also odd for an astromech

They are both often noted for their "bravery" or "courage"

In fact they are repeatedly honored for it on the same level as their human counterparts:

Amidala even makes R2 her personal servant. Because queens need .... astromechs?

Chewbacca goes out of his way to save Threepio in ESB

Also,

They are the only witnesses to Anakin's wedding, which is a bit bizarre considering what a blabbermouth Threepio is.

This seems odd, and there only seem to be a few examples (HK-47 possibly?) where other droids behave in this manner or are treated this way. In fact, pretty much every other droid in the movies is little more than a prop.

So my question is:

Are C-3PO and R2-D2 different from normal Star Wars droids in some known in-universe way, or do all droids in the galaxy operate this way and are treated this way by others