Only wolves can be commanded to follow by E key (and you can ride a lox to move to another/new base but won't spoil how - can google it).

Boars, once tame, just wander as they will - can't command them to follow you. You can push a boar using your char body but they only move so far before they become startled and then start running randomly.

So if body pushing you can only shove short distances, like off a dock into a boat if you want to transfer a 2 star boar to main base,etc.

Only way I've been able to effectively move boar is by building a 1 tile wide corridor out of wood pieces from A to B

e.g. if tamed at Base A and want to get boar to base B - build wood lane from pen to dock with small ramp dropping down to ship, shove boar from pen into lane, shove boar down lane and periodically create a divider behind you because once they startle from being shoved too much they can run randomly. Push down onto boat, ferry them to base B.

get boar out of boat using ramps or destroy boat (haven't really done this option, might kill boar) and same lane process to new pen.

If base B is not accessible by boat and is overland, then not sure what to tell you - normally I wouldn't move a boar to land base this way, and just run the wild boar from where it spawned to cage pen in that base.

Wolves are lot easier. Tame anywhere, then use E command to make follow you and can lead tame wolves as you like. Same caveat about getting onto boats and off though, need a ramp built or destroy boat.