As Swish Horse is a registered trade mark for Horse Rugs - as in Swish Horse Rugs - then no I do not believe they are different and Swish Rugs would not be able to be registered as a trade mark for horse rugs.
As Swish Horse is a registered trademark for horse rugs owned by Swish Horse Pty Ltd and registered in 1997, I suggest you contact the trademark owner before you offer any sponsorships under this brand.
I think you need to start with a new name for your rugs.
Swish Horse Rugs already exist (see www.swishhorse.com) and Swish Horse is a registered trade mark for Horse Rugs.
I think you need to start with a new name for your rugs. Swish Horse Rugs already exist (see www.swishhorse.com) and Swish Horse is a registered trade mark for Horse Rugs.