3713011 object (that is the internal SPICE/SPK id) is a special trajectory computed by the New Horizons team at SwRI which included data which is not in the public domain. The other one for
(486958) 2014 MU69 (its official asteroid number and temporary discovery designation) is for the publicly available data.
Generating an ephemeris in HORIZONS for the former produces:
Revised: Dec 29, 2018 486958 (2014 MU69) 2486958
This pre-computed trajectory is consistent with the New Horizons spacecraft
Kuiper-Belt extended mission, with the planned 3500 km flyby of Ultima Thule
on 2019-Jan-1 @ 05:33 UTC.
Trajectories were provided by the New Horizons mission planning team at SWRI
and are fits to internal flight-project data that has not been made available
outside the flight project.
To use this official mission trajectory to ...
A) Generate ephemerides with respect TO the mission target:
Specify the coordinate center in Horizons as "@2486958"
B) Generate ephemerides OF the mission target
Specify the target in Horizons as "2486958".
To instead use the latest JPL ground-based orbit solution (based on the
publicly available data) and numerically integrate over an arbitrary
time-span with statistical uncertainties of that public dataset, do a
look-up in Horizons with syntax "2014 MU69;" or "486958;" or "DES= 2486958;"
or "DES= 2014 MU69" or "2486958;" (i.e., with a semi-colon).
Note: the object previously had a provisional SPK ID of 3713011. It was
then assigned an IAU number of 486958 such that the primary SPK ID became
the present 2486958 (2000000 + IAU number).
Trajectory name Start (TDB) Stop (TDB)
--------------------------------------- ----------------- -----------------
20180601_20250101_od141_tcm30_burn_V0.1 1994-Jan-08 00:00 2033-Dec-21 00:00
(486958) is 2014 MU69's official number and is used at e.g the MPC. 3713011 and 2486958 are the JPL SPK id's for the kernels with and without the extra trajectory information respectively; they are not used outside JPL's software such as HORIZONS, Small Body Browser or the SPICE toolkit. Tutorial 18 of the SPICE Tutorial covers SPK files if you want more details.
The JPL software system handles multiple versions of the trajectory and/or orbital elements by creating multiple "bodies" for the same object. This is most commonly seen with comets which have 1 or more orbital elements for each perihelion passage e.g. this screenshot for comet 46P (Wirtanen):