The Richmond Shipyard Railway and Parr Terminal are two different things. The RSRY was a WWII transit operation run by the Key System on behalf of the US Maritime Administration from 40th & San Pablo in Emeryville to Kaiser's shipyards in Richmond. Parr had several terminals: one at the foot of Adeline St in Oakland, which had its own locomotive(s), another in what became the Oakland Army Base, and a third in Richmond near the Kaiser shipyards.

The pic shows the intersection of South Harbor Way (left-right street) and Wright Ave, which upon checking is about 1/2 city block south of where the RSRy started using this alignment to shift from paralleling Potrero Ave northward to paralleling Cutting Blvd (virtually all traces of the RSRy along Potrero were obliterated by the construction of the freeway).

Th RSRy was double track, electrified. The ownership of a lot of trackage in this area of Richmond is quite complicated, which has been compounded by the passage of time since WWII.

The wye under the Richmond Parkway overpass near Ohio Ave is the former connection to the Santa Fe's line through El Cerrito and Berkeley to Emeryville, which paralleled Ohio all the way to San Pablo Ave. This was the former California and Nevada RR, a narrow gauge line which Borax Smith acquired to obtain the tideland rights for building what became the Key Route Pier. He sold the rest of the RR between Emeryville and Richmond to the Spreckels interests, who were building what became the Stockton Sub of the AT&SF. The Santa Fe used this wye to turn its passenger trains. When the line through Berkeley was abandoned (the franchise was about to expire, and traffic had dropped perciptously), it was reconfigured to its present connection over portions of the RSRy's former route to SP's water side drill at Stege.

The Richmond Belt Line was the railroad which served the Standard Oil refinery and out the other side to serve a whaling station, a tank car faciility, the Navy's fuel depot at Point Molate (formerly a winery called Winehaven), and finally ending up at a quarry at what is now the east end of the Richmond-San Rafael Bridge, almost but not quite making a full circle to the Santa Fe's trackage near the Standard Oil Piers a little bit further south. Operation was traded between the SP and AT&SF every so many years until the late 1980s, when a new contract operator appeared on the scene. After a few corporate shuffles, this is what has become the "Richmond Pacific". The 1980s was the beginning of the end for the craft of switchmen on both RRs, and I have a vague recollection that may have spurred the two RRs into being willing to terminate the trading agreement. I'm not sure just how the RP came to operate other trackage outside of the refinery, nor whether there has been changes to the ownership of any of the trackage.

And BTW, that wikipedia article is incorrect when it refers to the cars at Rio Vista Junction as the "oldest electric cars in existence" (the cars themselves were built as steam trailers in 1887). They are the oldest operable electric rapid transit cars. They were electrified between late 1902 and early 1903 as part of the first step of electrifying all the elevateds in NYC. The Shore Line Trolley Museum has an older one, 1872, but it was demotorized and used as an employee pay car long before leaving the NYC system for the Museum. They have to tow it around, and only on very special occasions. At the moment, the two at Rio Vista are out of service pending repairs.