Gaudiya Math was founded by Bhaktisiddhanta Sarasvati while his disciple Srila A.C. Bhaktivedanta Swami Prabhupada founded the ISKCON. Both organisations are Gaudiya Vaishnavism based. My question is whether there are any key differences regarding the philosophies, theology, practices, beliefs and teachings of Gaudiya Math & ISKCON.
Gaudiya Math was founded by Srila Bhaktisiddhanta Sarasvati Prabhupada in the early 1900s. During his lifetime he initiated over 60,000 disciples, many of whom are well-known proponents of Gaudiya Vaishnava siddhanta, such as Srila A. C. Bhaktivedanta Swami Prabhupada, Srila Bhakti Rakshaka Sridara Goswami, Srila Bhakti Prajnana Keshava Maharaj, Srila Bhakti Dayita Madhava Maharaj, Srila Bhakti Srirupa Siddhanti Maharaj, and many others.
After the departure of Srila Bhaktisiddhanta Sarasvati Prabhupada in 1937, there was some turmoil and fragmentation of the Gaudiya Math into various groups such as Sri Chaitanya Math, Sri Chaitanya Gaudiya Math, Sri Gaudiya Vedanta Samiti, Sri Chaitanya Sarasvat Math, etc. However, these are known collectively as Gaudiya Math because they hold a number of central tenets of Gaudiya Vaishnavism in high regard, and all accept Srila Bhaktisiddhanta Sarasvati Prabhupada as the prominent authority and guru (or parama-guru, parat-parama-guru, etc) in the Gaudiya Vaishnava line. For the purposes of this discussion, we'll continue to refer to this group of organizations as "Gaudiya Math" as they are effectively unified in core matters of tattva and siddhanta (philosophical truths and scriptural conclusions).
One disciple of Srila Bhaktisiddhanta Sarasvati Prabhupada was initiated as Abhaya Caranaravinda. After the departure of Srila Bhaktisiddhanta Sarasvati Prabhupada he was given the title "Bhaktivedanta" and often known as Bhaktivedanta Prabhu (being a householder and later a vanaprastha). In the 1950s he accepted sannyasa from Srila Bhakti Prajnana Keshava Maharaj (founder of Sri Gaudiya Vedanta Samiti), and took the sannyasa name Bhaktivedanta Swami Maharaj. After this time he used the name "A. C. Bhaktivedanta Swami" in his publications. Later, after coming to America in 1965 and founding the International Society for Krishna Consciousness (ISKCON), he allowed his young western disciples to call him Prabhupada, so his name appears in later publications (per his instructions) as A. C. Bhaktivedanta Swami Prabhupada.
This long-winded biographical preamble is important because it is specifically over the use of the title "Prabhupada" (one at whose feet there are many prabhus or elevated persons) that the first serious disagreements arose between Srila A. C. Bhaktivedanta Swami Prabhupada and his Godbrothers in the various Gaudiya Maths, who had previously agreed that only Srila Bhaktisiddhanta Sarasvati Prabhupada would be referred to by the title "Prabhupada." These disagreements were in some cases fairly acrimonious but the Founter-Acharya of ISKCON declared in 1976 or 1977 that "the war with the Gaudiya Math is over."
At no time did Srila A. C. Bhaktivedanta Swami Prabhupada indicate in his books even the slightest difference from what was taught by his gurudeva Srila Bhaktisiddhanta Sarasvati Prabhupada, and in fact quoted extensively from Srila Prabhupada Sarasvati Thakur's commentaries in his own purports.
There were some philosophical ideas which achieved a type of urban legend status in ISKCON, especially before publication of the Seventh Canto of Srimad-Bhagavatam in 1976. Most prominent among these urban legends was the interpretation that since our svarupa or constitutional position is to be with Bhagavan Sri Krishna in Goloka Vrindavan (Vaikuntha), we must have fallen from there since there are many scriptural references to our position being patita or fallen. However, Srila A. C. Bhaktivedanta Swami Prabhupada set this straight in the translation and purport to Maharaj Yudhisthira's inquiry to Devarshi Narada during the Rajasuya Yajna in the Seventh Canto of Srimad-Bhagavatam, in connection with the story of Jaya and Vijaya being cursed by the four Kumaras.
Thus, while those who looked to Srila Prabhupada's books considered the matter settled, others did not, and this was later (in the 1990s, long after Srila Prabhupada's departure in 1977) presented as siddhanta (but not accepted by many members of ISKCON). After some considerable turmoil and some scandals in the 1980s, ISKCON sought to solidify its institutional boundaries and voted on certain points such as the origin of the jivatma, with conclusions differing from Gaudiya Math (and other Vaishnava sects as well). There are many leaders and senior devotees in ISKCON even today who do not accept these later doctrines such as the idea that the jivatma (soul) originated from Vaikuntha rather than from the tatastha (marginal) region. However, those who disagree do so quietly.
It is thus a question whose answer will differ depending on whom you ask, and the official position of the institution ISKCON on philosophical questions may certainly differ from many persons who still consider themselves part of the ISKCON that was founded by Srila A. C. Bhaktivedanta Swami Prabhupada. So the short answer is, "going by Srila Prabhupada's books, no, but it really depends on whom you ask."
There are other finer points such as the qualifications of a guru, what are the qualifications for practice of the different types of bhakti-sadhana (devotional practice), what is the definition of vaidhi-bhakti, raganuga-bhakti, and ragatmika-bhakti, etc. Interestingly, many of these points are addressed in the book From Copper to Touchstone by Sripad Satsvarupa das Goswami, a senior ISKCON member, which was written after Satsvarupa Maharaja's own association with Srila Bhaktivedanta Narayana Maharaj, a prominent disciple of Srila Bhakti Prajnana Keshava Goswami and member of Gaudiya Vedanta Samiti (one of the Gaudiya Maths per the definition accepted for this discussion). In the book From Copper to Touchstone, Satsvarupa Maharaj goes through Srila A. C. Bhaktivedanta Swami Prabhupada's translations and purports to Sri Caitanya Caritamrita and discusses many of these finer philosophical points as they are fairly well-known in Gaudiya Math (but not that well-known in ISKCON as Srila Prabhupada departed this world not long after completing publication of Sri Caitanya Caritamrita in 1975. For those not familiar with it, Sri Caitanya Caritamrita of Srila Krishnadas Kaviraj Goswami (written in Bengali with numerous Sanskrit verses) is a central philosphical work of Gaudiya Vaishnavism.
In summary, it is a sensitive and complex set of issues which is guaranteed to arouse strong opinions based on the perspective of the speaker. My own perspective should be no secret, as I am an initiated disciple of Srila A. C. Bhaktivedanta Swami Prabhupada and also of Srila Bhaktivedanta Narayana Maharaj (in Gaudiya Math and in ISKCON, there are two parts to initiation). I have always looked to Srila Prabhupada's books as the authority to settle philosophical discussions, and consider them to be a complete representation of Gaudiya Vaishnava siddhanta (with many references to "must read" sources such as Brihad-Bhagavatamrita and Shat-sandarbha). Additionally, I have heard extensively from Srila Bhaktivedanta Narayana Maharaj and many of his siksa disciples and at no time have I found any philosophical point which contradicts anything in Srila Prabhupada's books. There are many deep philosophical topics mentioned briefly in Srila Prabhupada's books such as advaya-jnana-para-tattva and akhanda-guru-tattva, and they are expanded based on writings of Gaudiya Vaishnava acharyas such as Srila Rupa Goswami, Srila Sanatana Goswami, Srila Jiva Goswami, Srila Vishvanath Chakravarti Thakur, Srila Baladeva Vidyabhushana, and many others.