Dovetail bases/rings whether from Redfield or Leupold are 'interchangeable'. I wouldn't mix a front Redfield with a rear Leupold, but you get the idea. Would recommend that if you get Redfield bases then you also get Redfield rings, but not a requirement.
Redfield originated the system with either a one or two piece base with rotary dovetail front ring and windage adjustable rear ring held by dual opposing screws. It was an extremely popular mounting system and when the patents ran out, other companies began manufacturing it. I have seen these mounts made by Redfield, Leupold, Burris, Millett and there must be others.
It is a pretty standardized system and you can use Burris rings on a Leupold base and so forth. However, as Shawn has stated, don't mix one brand of front ring with another brand of rear ring because the heights are probably different.
Weaver designed a different mounting system with one or two piece cross-slotted bases and clamp on rings with a transverse bolt that fits the cross slot on the base. When the patent on that ran out, just about everybody started making that system as well.
In the case of Leupold, for example, you can get the standard bases and rings that are the Redfield style. You can get a Dual Dovetail system that has the rotary dovetail ring both front and back (it is stronger than the ones that have the windage adjustable rear base for heavy recoiling rifles), you can get the QRW (Quick Release Weaver) style bases and rings that are interchangeable with the Weaver system, and you can get Leupold's own quick detachable system that is different than all of them.
So there are two major scope mounting systems (plus several others not quite so popular), the Weaver and Redfield systems...but you can buy them from many different companies.
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