Not discerning the body ijn 1 Cor. 11 is contextually referring to not recognizing other believers as members of the body that Christ purchased with His own blood, (Acts 20:28) by eating independently and even to the full in the communal feat that the Lord's supper was, ignoring others hungry and shaming them that have not. Therefore while they came together to eat the LS, in fact,
When ye come together therefore into one place, this is not to eat the Lord's supper. For in eating every one taketh before other his own supper: and one is hungry, and another is drunken. What? have ye not houses to eat and to drink in? or despise ye the church of God, and shame them that have not? What shall I say to you? shall I praise you in this? I praise you not. (1 Corinthians 11:20-22)
For as often as ye eat this bread, and drink this cup, ye do shew the Lord's death till he come. (1 Corinthians 11:26)
To eat together in a religious feast signified communal unity with the one it was to honor, and thus Paul warns them against having fellowship with devils by taking part in their pagan feasts - but not because such food became the flesh of devils. (1 Corinthians 10:20) And Paul treats "remember" as to act that out (cf. 1Co. 15:1,2) and thus they were to show/declare the Lord's death by showing communal unity with and love for Christ and each other who were bought with His blood, they being the ones who effectually realized what Christ was bruised/broken and pouring out his soul for. (Isaiah 53:10,12). And as Paul learned, how you treated His body, the church, was how you treated Christ. (Acts 1:4)
However, the Corinthians were acting exactly contrary to what they were supposed to be showing, selfishly ignoring others, not discerning the church as the Lord's body which Christ bought with His own blood, and which body is the focus both here and in the next chapter.
While the often seen practice of Catholics receiving the wafer and sip of wine and then leaving is understandable in the light of their false doctrine with its emphasis upon the elements consumed, even in many Prot churches the LS is that of (hopefully) repenting from personal sins from solemnly consuming a bit of bread and juice in abstractly thinking about the Lord's death, but with little understanding and consciousnesses of the communal unity that is sppsd to be showing by sharing bread as members of the body which Christ bought with His blood.
Could be a double meaning there.
I must commend you in your own discernment of making this distinction. It is one that is continually mispreached that "the body" here is the "bread loaf" somehow transubstantiated into human flesh.
This is a reversal of the correct doctrine in which an assemblage of persons gathered for a purpose is a "body" of people, and when that assemblage is the ones called out (summoned) to Remember the Lord and His Death together, the whole bread loaf does symbolize that assembly, which itself symobolizes the working of a human body--in this case, the body of humans aggregately operating to comport itself according to the will and direction of its Head, the Lord and King Jesus Christ.
This issue is related to another verse in this book, 6:19, in which the grammar demands that the body described there is the assemblage of living persons, of which the individuals are symbolized by the stones of a structure, the structure being envisioned as a Temple of the Holy Ghost of living stones (1 Pet. 2:5).