"Unbelief was taking possession of their minds and hearts. Love of honor had blinded them. They knew that Jesus was hated by the Pharisees, and they were eager to see Him exalted as they thought He should be. To be united with a teacher who could work mighty miracles, and yet to be reviled as deceivers, was a trial they could ill endure. Were they always to be accounted followers of a false prophet? Would Christ never assert His authority as king? Why did not He who possessed such power reveal Himself in His true character, and make their way less painful? Why had He not saved John the Baptist from a violent death? Thus the disciples reasoned until they brought upon themselves great spiritual darkness. They questioned, Could Jesus be an impostor, as the Pharisees asserted? DA 380.1"
"When Jesus therefore perceived that they would come and take him by force, to make him a king, he departed again into a mountain himself alone."
Both passages discuss the disciples' expectations of Jesus as a king and their disappointment when He doesn't fulfill those expectations in the way they anticipate. EGW elaborates on the disciples' reasoning and doubts, which are prompted by Jesus's actions in John 6:15.
"The disciples had that day witnessed the wonderful works of Christ. It had seemed that heaven had come down to the earth. The memory of that precious, glorious day should have filled them with faith and hope. Had they, out of the abundance of their hearts, been conversing together in regard to these things, they would not have entered into temptation. But their disappointment had absorbed their thoughts. The words of Christ, “Gather up the fragments, ... that nothing be lost,” were unheeded. Those were hours of large blessing to the disciples, but they had forgotten it all. They were in the midst of troubled waters. Their thoughts were stormy and unreasonable, and the Lord gave them something else to afflict their souls and occupy their minds. God often does this when men create burdens and troubles for themselves. The disciples had no need to make trouble. Already danger was fast approaching. DA 380.2"
"When they were filled, he said unto his disciples, Gather up the fragments that remain, that nothing be lost."
EGW directly quotes John 6:12, making this an explicit allusion. The surrounding context in DA 380.2 also references the events described in John 6:12.
"A violent tempest had been stealing upon them, and they were unprepared for it. It was a sudden contrast, for the day had been perfect; and when the gale struck them, they were afraid. They forgot their disaffection, their unbelief, their impatience. Everyone worked to keep the boat from sinking. It was but a short distance by sea from Bethsaida to the point where they expected to meet Jesus, and in ordinary weather the journey required but a few hours; but now they were driven farther and farther from the point they sought. Until the fourth watch of the night they toiled at the oars. Then the weary men gave themselves up for lost. In storm and darkness the sea had taught them their own helplessness, and they longed for the presence of their Master. DA 380.3"
"But the ship was now in the midst of the sea, tossed with waves: for the wind was contrary."
Both passages describe the disciples in a boat, struggling against a storm. The EGW passage elaborates on the disciples' fear and helplessness, which is implied in Matthew's account.