Web company wants to move registrar for new site

[Brother D]

So I own a domain, and we're not happy with the existing website provider, and we've found a new one who seem to have good ideas.
However they want us to transfer the registrar aspect over to them, and seem quite insistant. I've always handled the forward and records myself, but I'm a bit hazy on what would happen if we move registrar further down the line and want to move the domain elsewhere...

As I am listed as the registrant, I assume I can recover the domain at a later date if need be? Or would you advise to leave the domain with the existing registrar and update the records there?

Thanks in advance.

[Brother D]

So this is where it's a bit hazy with seeemingly people using registrar and registrant inter-changably. So basically you keep the domain registered say at Register1, but migrate to the new registrar such as go daddy?

I'm just looking to avoid them sitting on a domain if we want to move and holding us to ransom.