If you are in single-ended mode using RCA termination, then you do not have to worry about a separate ground between phono and linestage. The interconnection does that. However you likely but not always need a separate ground wire between tonearm and phono. It serves to provide earth ground between phono chassis and TT or tonearm. Many but not all dedicated phono ICs provide that ground wire as a separate wire with a forklike connector that goes to the ground lug on your phono stage.
Some TT's ground through the shield on one channel, like my Thorens 165. Simply adding a ground wire might make a "loop" and introduce hum. Go to vinyl engine and down load your shop manual. TT signal voltage is much lower than line inputs, Maybe here you want to stick with TT leads, OEM or aftermarket
It is ONLY the Cartridge/Tonearm that needs to be grounded. No separate ground wire is needed from Preamp to Amp
A typical Phono Cable has an integral ground wire
Separate Ground Connectors (various types of wire attachment terminals) exist at both ends/both devices for the ground wire of the Phono Cable. Labeled GND, or something like that.
ANY ’real’ Phono input receives the cartridge’s low level un-equalized signal and a ground connection must exist, typically adjacent to the ’phono’ input (not always adjacent, it can be somewhere else on the back of the input device).
Other ’non-real’ Phono Inputs exist, but they are simply ’named’ Phono, for the convenience of front selector input names. They are ’line level’ inputs, requiring the cartridge’s low level and un-equalized signal to have been converted to line level elsewhere. No ground wire is needed for those ’non-real’ phono inputs.
Typically, if you see the rear panel, and a pair of rca jacks exist labeled phono, if there is no adjacent separate ground connector, it is a ’non-real’ ’named’ phono input.
Careful research of any device is required to determine if the device contains a ’real’ phono input of the cartridge’s low level signal or a ’non-real named’ phono input of an already equalized/boosted to line level signal strength.
A true balanced phono connection from cartridge to phono inputs to a balanced phono stage nearly always does not need a separate earth ground wire. (3 of my 3 balanced phono stages do not require a ground connection.) Typically, ground floats in such a connection. Typically also a balanced phono will offer XLR inputs. Also, to amend what E wrote, sometimes the TT itself may need to see common ground not just the tonearm, in SE mode.
The Cartridge is a balanced device is not grounded although some designs may ground the shell of the cartridge through the mounting points. It is the tonearm that is grounded. This is by a single wire that goes from the tonearm to the phono stage or preamp. As @theflattire seems to have noticed sometimes it is not necessary to connect the ground and in some instances it might even be quieter without the ground wire connected.