They occur in the same place but not at the same date. "Remembrance of the Daleks" shows that it takes place after the Doctor, Susan, Barbara & Ian had left Shoreditch in "An Unearthly Child". This is especially clear when the Seventh Doctor visits the undertaker to collect the coffin, containing the Hand of Omega, that had been left behind by "an old geezer with white hair" (the First Doctor).
It's not made clear how long after the First Doctor's departure "Remembrance..." takes place but it cannot be very long, because the history book that Susan left in Ian's science classroom had not been tidied away -- Ace found it still in the science classroom (however as the two books have different covers, it's possible this was a different book. The rooms do not match either).
It's not even clear that it takes place before the First Doctor and Susan left. The First Doctor and Susan left Earth in November 1963. The Seventh Doctor and Ace arrive in 1963. in magnificent sunshine. And it's still bright outside in the evenings. Furthermore the junkyard they land in states "IM Forman" rather than "IM Foreman"(as it does in "An Unearthly Child"). "Interference Book Two" (novel) explains that the junkyard was actually a travelling TARDIS-like machine, and it didn't immediately take on its new appearance, but rather took some time to fully form its outward appearance. These all suggest that "Remembrance of the Daleks" actually takes place earlier in 1963 than "An Unearthly Child" does.