Definition from Google
the point in the orbit of a planet, asteroid, or comet at which it is closest to the sun.
Apsis denotes either of the two extreme points (i.e., the farthest or nearest point) in the orbit of a planetary body about its primary body (or simply, "the primary").
Also from Wikipedia:
For generic situations where the primary is not specified, the terms pericenter and apocenter are used for naming the extreme points of orbits
As @Rory notes, periapsis is also a relevant term which, according to Wikipedia, is preferred to pericenter in technical usage. Likewise with apoapsis, I would add. But Wikipedia notes these terms can also be used to refer to distances rather than points.
"An inferior conjuction occurs when the two planets lie in a line on the same side of the Sun."
I have not found any terms referring to the two different portions of the orbit of two bodies, between the nearest and furthest points.