Not exactly.
Relaxer should never be applied anywhere but the new growth (unless it's a corrective relaxer to fix underprocessed portions or a virgin relaxer), and it especially should not be combed through. When that happens, the ends get very overprocessed and end up weak, dry, dull, brittle, and eventually break off.
The difference between relaxing and texlaxing is just that when the hair is texlaxed, the relaxer is purposefully rinsed out early, there is still visible texture left in the hair. Hair that is fully relaxed is definitely closer to bone straightness.
Texlaxing the hair has the benefit of looking more interesting, it tends to have more fullness, and stretching can be easier because there's less difference between the relaxed part and the new growth. Also, texlaxed hair generally is exposed to relaxer for shorter periods, so the protein bonds are less broken, and therefore, texlaxed hair has a slight health advantage over relaxed hair. But I think it can be harder to detangle, and it can be hard to get a uniform texture throughout the hair. Also there is shrinkage involved, but that can be a good thing, depending on what someone likes.
Relaxed hair has the benefit of having a uniform texture throughout the hair, there tends to be fewer issues with detangling, no shinkage (but that can be good or bad), and it's easier to wear straight styles.
The disadvantage to relaxed hair is that the hair tends to be less full because there's no texture, the hair is exposed to relaxer for longer periods of time, and stretching can be harder because of the disparity between the natural texture and the relaxed hair.
hth!
