The slow solar wind is typically characterized as having low Alfvenicity. However, Parker Solar Probe (PSP) observed predominately Alfvenic slow solar wind during several of its initial encounters. From its first encounter observations, about 55.3% of the slow solar wind inside 0.25 au is highly Alfvenic ($|sigma_C| > 0.7$) at current solar minimum, which is much higher than the fraction of quiet-Sun-associated highly Alfvenic slow wind observed at solar maximum at 1 au. Intervals of slow solar wind with different Alfvenicities seem to show similar plasma characteristics and temperature anisotropy distributions. Some low Alfvenicity slow wind intervals even show high temperature anisotropies, because the slow wind may experience perpendicular heating as fast wind does when close to the Sun. This signature is confirmed by Wind spacecraft measurements as we track PSP observations to 1 au. Further, with nearly 15 years of Wind measurements, we find that the distributions of plasma characteristics, temperature anisotropy and helium abundance ratio ($N_alpha/N_p$) are similar in slow winds with different Alfvenicities, but the distributions are different from those in the fast solar wind. Highly Alfvenic slow solar wind contains both helium-rich ($N_alpha/N_psim0.045$) and helium-poor ($N_alpha/N_psim0.015$) populations, implying it may originate from multiple source regions. These results suggest that highly Alfvenic slow solar wind shares similar temperature anisotropy and helium abundance properties with regular slow solar winds, and they thus should have multiple origins.