So did Slate make the Booker/Comstock connection or what? If he could remember Booker from Wounded Knee, but existed in Comstock's reality, what exactly did he think was going on?!
As you probably know comstock is booker but just in a trans-dimensional world, so comstock fought at wounded knee with slate. Because comstock is genetically speaking the same person as booker dewitt, so they obviously look the same.
But because zachary hale comstock has been over using the trans-dimensional tear machine created by rosalind lutece, it has left him ill, OLDER LOOKING, and sterile (unable to conceive) and then booker dewitt gets transported to the floating utopia that is columbia, he obviously looks the same as comstock, but 20 years older, and because comstock looks a lot older than he actually is, slate doesnt recognise him, but recognises booker.
Because the game contains concepts of time travel, inter-dimensional travel, infinite universes etc it just so happens that our booker dewitt fought at wounded knee as well but in his own universe. Like for example when you crossover with elizabeth at chen lin's gunshop you transport through the tear they are virtually the same apart from the obvious vox populi rise and even songbird is there, just goes to show that even though your transport to a different dimension it can be very subtle or as dull as dishwater.