Terminology In Social Biology: Cooperation= Intraspecific...Mutualism= Interspecific?

My query to Trivers:

Currently, there is a discussion on Twitter regarding proper usage of the term, "mutualism". 

In my training, "mutualism" is reserved for Interspecific interactions, "cooperation" for Intraspecific interactions.

It seems that in the Ecology literature, "mutualism" is reserved for Interspecific interactions but that in the Behavior literature, "mutualism" and "cooperation" appear to be used interchangeably.

Please "weigh in" on this terminological issue, permitting me to quote your reply.

Thank you for your attention to this post.  

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Response from Robert Trivers:

yes i am used to your distinction but have paid no attention to the word
or its use for many years

mutualiism classically was between species, neither harm nor benefit
given, or when benefit not to the level of a symbiosis

Clara B. Jones Comments On Terminology In Social Biology (YouTube)

https://www.youtube.com/watch?v=o0cMyWzB33o&feature=youtu.be

Summary of Comments:
1. Terminology in Social Biology not standardized across taxa from social microbes to humans.
2. Want standardized terminology for comprehensive Science of Social Biology and for formulation of general models ("laws", principles, treatments, statements) of Social Biology.
3. Comments pertain primarily to empirical literature since theoretical treatments are usually clear about notation and assumptions.
4. Comments pertain primarily to vertebrate literature since social insect literature generally utilizes Hamilton's 4-way schema defining conspecific interactions based upon differential reproductive costs and benefits*.
5. Two primary concerns at this time. First, usage of word "social".
6. "Social" used in 4 ways in literature:
a. grouped or clustered Population Structure (Spatial Ecology or Population Genetics);
b. any interaction between/among conspecifics;
c. any "positive" interaction between/among conspecifics (e.g., helping, many non-damaging responses);
d. an interaction whereby an Actor facilitates the reproduction* of a conspecific Recipient; this is W.D. Hamilton's definition, the definition that I advocate.
[1] usage of "positive" interaction is problematic;
[2] most researchers assume "positive" interactions are induced by cooperation or altruism;
[3] Hamilton defined "cooperation" as an interaction in which both Actor & Recipient benefit reproductively, defining "altruism" as an interaction in which the Recipient benefits at the expense of the Actor's reproduction;
[4] in Hamilton's system, Cooperation & Altruism are the only forms of Social interaction among conspecifics;
[5] problematically, "positive" interactions may be induced not only by Cooperation or Altruism but, also, by Selfish responses which Hamilton defined as an interaction among conspecifics whereby an Actor benefits reproductively at the expense of a Recipient;
[6] thus, we cannot assume that "positive" responses are necessarily induced by Cooperation or Altruism as is generally assumed in the literature;
[7] researchers, then, must differentiate between "positive" interactions induced by Cooperation or Altruism and "positive" interactions induced by Selfish responses (e.g., by coercion, force, persuasion, or exploitation [e.g., manipulation, "social parasitism").

*Reproductive costs and benefits may be measured as, for example, differential offspring mortality, number, quality, inter-birth-interval. See Lehmann & Keller (2006, JEB).