  Studying the relative orientations of the orbits of exoplanets and
wide-orbiting binary companions (semimajor axis greater than 100 AU) can shed
light on how planets form and evolve in binary systems. Previous observations
by multiple groups discovered a possible alignment between the orbits of visual
binaries and the exoplanets that reside in them. In this study, using data from
\textit{Gaia} DR3 and TESS, we confirm the existence of an alignment between
the orbits of small planets $(R<6 R_\oplus)$ and binary systems with semimajor
axes below 700 AU ($p=10^{-6}$). However, we find no statistical evidence for
alignment between planet and binary orbits for binary semimajor axes greater
than 700 AU, and no evidence for alignment of large, closely-orbiting planets
(mostly hot Jupiters) and binaries at any separation. The lack of orbital
alignment between our large planet sample and their binary companions appears
significantly different from our small planet sample, even taking into account
selection effects. Therefore, we conclude that any alignment between
wide-binaries and our sample of large planets (predominantly hot Jupiters) is
probably not as strong as what we observe for small planets in binaries with
semimajor axes less than 700 AU. The difference in the alignment distribution
of hot Jupiters and smaller planets may be attributed to the unique
evolutionary mechanisms occuring in systems that form hot Jupiters, including
potentially destabilizing secular resonances that onset as the protoplanetary
disk dissipates and high-eccentricity migration occurring after the disk is
gone.
