reply to baffled
Re: Hot water heater leaking from base? OP Did you try to determine where the water was leaking from on both the WH and Softener? The bottom outside skin doesn't look like it. If the tank were leaking the bottom of the housing would be wet along with the insulation and rusting out.
Or you could just replace them both due to age. Essentially they're at the end of their service life.