Has been going on for over a year on & off ... is either problem urgent?
Given that you have waited for a whole year it doesn't seem to be urgent to you.
If a water heater is nice enough to indicate imminent demise with a slow leak then I consider it urgent to replace it. It will not remain a slow leak forever and you could face considerable water damage when the water heater dies.
There is nobody here that can tell you from just looking at that picture whether or not you have one or two problems. You also didn't indicate whether both leaks started at the same time ? How is the slope of the floor in that room ? Are you sure water is draining from both water softener and water heater towards the bottom of the picture or is it possible that either of those appliances is a low point where water accumulates ?
All water heaters have a T&P safety valve that may release water when it is either too hot or the water pressure too high. The T&P valve is not visible in the picture but it seems that the vertical pipe on the right side of the water heater might be going to the T&P valve. A simple test to see if the water is coming out of the T&P valve (instead of a leak in the water heater) is to put a cup under the opening of that pipe. If the water is coming from the T&P valve you may have a bad water heater thermostat (water gets too hot at times) or too much water pressure (bad pressure regulator, expansion tank needs maintenance or not present but needed).
Some water softeners have an automatic self cleaning cycle that flushes water backwards through the filter element. Does your water softener do that and where does the water from the cleaning cycle drain to ? If it simply drains to the floor it may explain what appears to be a leak. -- Got some spare cpu cycles ? Join Team Helix or Team Starfire!
I found the softener is leaking at the neck of the unit, so we'll figure out whether that is repairable.
On my softener resin tank this is just a threaded connection with a large o-ring. The o-ring may have been compressed beyond the limit, or the resin tank may have gotten knocked or rotated slightly while you were investigating the heater problem. Mine is just hand-tightened.
If you have to replace the o-ring, and the control head is still in good shape, you might want to replace the resin in the unit at the same time. Not a tough job but messy. -- USNG: 16TDN2870 Find your USNG coordinates: USNGWeb