Lakatos describes the three types of falsification--dogmatic, methodological and sophisticated. Did Popper hold to sophisticated falsificationism or is it a charitable interpretation of Popper? Some seem to think that he held to methodological falsificationism, but Lakatos seems to imply that Popper held to sophisticated falsification. Which is it?
In Popper's most widely read summary or introductory piece, “Conjectures and Refutations,” the position sounds like Lakatos's “dogmatic falsificationism.” However, the position Popper actually developed in Logic of Scientific Discovery is close to Lakatos's “methodological falsificationism,” as Lakatos describes it in “Falsification and the Methodology of Scientific Research Programmes.”
Lakatos's “sophisticated falsificationism” incorporates his account of scientific progress. I understand Lakatos's account of theory choice as different from Popper's. Lakatos's emphasizes the rate of change of the ratio of successful predications to theory growth, while Popper basis his account of theory choice on an account of verisimilitude (see SEP discussion here).
So, I would suggest there are significant differences between Popper's view and Lakatos's sophisticated falsificationism. Lakatos personally, e.g. in his published letters with Paul Feyerabend, adopted a stance of opposition to Popper, along with reverence. So, while the similarity is a matter of degree, I would suggest there are sufficient differences to understand them as different positions.