Caption: A cartoon of a gravitationally-bound 2-body system with the spherically-symmetric bodies orbiting in elliptical orbits the system center of mass (i.e., barycenter in the context of celestial mechanics) marked by a red cross. The barycenter is a focus for both elliptical orbits and is at rest or in relative to an inertial frame. The other focuses for the elliptical orbits are just empty points in space.
Features:
The two kinds of apsides: periapsis and apoapsis.
A physical fact for orbits is that astro-bodies move slowest at apoapsis and fastest at periapsis.
r_mean = (1/2)( r_periapsis + r_apoapsis ),
where r_periapsis is the periapsis separation and r_apoapsis is the apoapsis separation.
r_periapsis = r_mean*(1 - e) and r_apoapsis = r_mean*(1 + e) ,
where e is the eccentricity of the relative elliptical orbit.
The actual elliptical orbits relative to the barycenter are scaled down versions of the relative elliptical orbit. The scale radii for any epoch are
r_1 = r*(m_2/m) and r_2 = r*(m_1/m) ,
where 1 is the index for astro-body 1, 2 is the index for astro-body 2, r is the relative separation distance, and m = m_1+m_2 is the total mass. As you can see, if m_1 >> m_2, we have r_1 ≅ 0$ and r_2 ≅ r. This just shows that if m_1 >> m_2, we effectively have astro-body 2 orbiting astro-body 1 which is effectively at rest at the barycenter.
Other than the example cases, if one wants a fancy name, yours truly suggests just prefix the name by peri- or ap-: e.g., peri-Jupiter and and ap-Jupiter.