No, they are the same as any other distal connection.
I don't think they are, because we are not allowing those connections to take place within the same columns.
Let's say we prevented cells from creating synapses to cells in the same column. So when the TM sees the C# active columns following a C# (same active columns), it would be unable to grow segments / synapses to the previous input.
Take the following sequence for example:
E - C#' - C#'' - C#'''
What we want is a temporal representation of each C# within the context of the previous input, like this:
C#' is C# in the context of E
C#'' is C# in the context of
C#''' is C# in the context of
C#' would be represented properly in the context of E because its active cells have formed synapses to cells in the active columns representing E. Now we must decide what cells should now be predictive for
C#'. If we disallow distal synapses between cells in the same column, no cells will ever become predictive in this time step because the previous spatial input only contained active cells within the same columns (and those connections are disallowed).
This would essentially lead to bursting columns for
C#''' every time it sees the sequence above.
EDIT: I am wrong, see below!