Relocating/Moving house

british-english

Relocating connotes a permanent move to an entirely new area (or even country) usually in order to take up a new job. Employment offers may include "relocation assistance" and wouldn't normally say "help with moving costs". In British English, it's jargon; and even relocate is defined in terms of move:

relocate

Move to a new place and establish one’s home or business there:
sixty workers could face redundancy because the firm is relocating
[with object]: distribution staff will be relocated to Holland

[ODO]

"Moving house" or simply "moving" is more common in British English than "relocating". There's even a website called HelpIAmMoving.com, which demonstrates the usage:

Moving house in is stressful. By thinking ahead and planning early it doesn't have to be as stressful. Here are our top tips...

Don't move on a Friday. Even though the weekend gives you time to settle in to your new pad, in reality it is the worst day of the week to move house.

Moving generally only means moving house, while keeping the same job and possibly other contacts, although it can indicate a permanent move entirely away. Relocation always means a permanent move entirely away.

I agree with @AndrewLeach that relocation means moving entirely away, usually with a change of job. For a specific word that means moving house, consider the verb flit (EOD reference here), which is still in wide use in Scotland and Northern England, and its noun flitting.

Denotations for 'relocate' differ according to which dictionary you choose to believe:

relocate ... v.i.

1. to change one's residence or place of business; move. [Random House Kernerman Webster's College Dictionary, © 2010]

vs

relocate v.intr.

To become established in a new residence of place of business: relocated in Ohio. [AHDEL]

Though I'd also be swayed in my choice of words by connotation.