How can we be sure that we have identified very distant stars correctly? From reading this question on calculating distance to stars and from a bit of background reading on the standard candle theory I still don't see how we can confirm that a star we see at one distance and a star we see at another distance (redshifted and at a different apparent luminosity) are the same type.

Beyond a certain distance, parallax is not possible, so how can we confirm star X and star Y are the same type therefore the difference in redshift and luminosity means Y must be at distance Z. How do we know it isn't a different type of star at a different distance?

Or are we just saying they look similar, so probably are?
We determine the spectral type (i.e. temperature) of a star using multicolour photometry, or (ideally) spectroscopy. By guesstimating the temperature, mass and radius of a star, we can say that two stars that have pretty similar observational properties probably are closely related to each other.

Cepheid variables, for example, display periodic pulsations that depend quite strongly on their intrinsic luminosity -- this is why they're reasonably good standard candles. Their characteristic variability makes them clearly identifiable as a Cepheid, and observations of their pulsation are backed up by data that place them in the same region of the HR diagram.

If it looks like a duck, swims like a duck, and quacks like a duck, then chances are it's a duck. If it's as hot as a Cepheid and pulsates like a Cepheid, then it probably is a Cepheid.

So to answer your final paragraph: yep. Though with no spatial resolution and often (in the absence of parallax measurements) only tenuous distance data, classifying stars is a rather messy business.