Probably by the grammatical perspective remediation means the act of correcting an error or a fault or an evil (whether it is a living thing or not, Ex: soil, air, water in general), where as healing means the natural process by which the body (a living thing) repairs itself or with the help of an external force.

I may not be correct but this is my view....  

Dear Abhijit,

Bioremediation is a waste management technique that involves the use of organisms to remove or neutralize pollutants from a contaminated site.

BioHealing is an industry leader in the science of regenerative medicine. The Company is focused on the commercialization of cell-based and tissue-engineered products. It currently markets the FDA-approved product Dermagraft.

Thanking  you

Bioremediation is the process whereby organic wastes are biologically degraded under controlled conditions to an innocuous state, or to levels below concentration limits established by regulatory authorities.

http://www.icontrolpollution.com/articles/bioremediation-an-overview-161-168.pdf

Biohealing is a wound care technique

https://www.google.co.in/url?sa=t&rct=j&q=&esrc=s&source=web&cd=80&cad=rja&uact=8&ved=0ahUKEwiGtZLG57zJAhXNB44KHXApBXM4RhAWCEEwCQ&url=http%3A%2F%2Fwww.pva.org%2Fatf%2Fcf%2F%257BCA2A0FFB-6859-4BC1-BC96-6B57F57F0391%257D%2FSaturday_Chua_Advanced%2520Wound%2520Care%2520Modalities%2520for%2520the%2520Treatment%2520of%2520Pressure%2520Ulcers.pdf&usg=AFQjCNFyXF6owgU41LKbEK5nRgED1NUSBg&sig2=-zT52a2PUXondXOi6RIpNw

Just a note of caution when using popular terms in multidisciplinary science: Due to different analytical methods applied in different fields (e.g. environmental microbiology vs. geochemistry) the meaning of the same term can differ considerably.  Besides, terms that were coined with the intention to promote emerging views in applied applied science may be subject to changes before finally getting established or agreed upon.

The term "Bio-remediate" means to use biological organisms to break down hazardous substances into less toxic or non toxic substances present in soil, water, wastes, contaminated material and any other component of the environment. Bioremediation provides a technique for cleaning up pollution by enhancing the same biodegradation processes that occur in nature. Depending on the site and its contaminants, bioremediation technologies viz., phytoremediation, bioventing, bioleaching, bioreactor, composting, bioaugmentation, rhizofiltration, and biostimulation may be safer and less expensive than alternative solutions such as incineration or land-filling of the contaminated materials. We can also call it Biohealing as through bioremediation is a way to improve/restore the health of degraded soil, water and ecological components by biological means.  

In medical terms, the term Biohealing is used for the treatment of diseased or damaged body parts with regenerative medicines.