Since Russian cities are often laid out differently from those in Western Europe, North America and elsewhere, the labels applied to various parts of the city may be specific to the Russian language and lack exact equivalents in other languages. The situation may be similar in other countries that use the Russian language.

Подъезд

The word подъезд consists of the prefix под- (proximity) and the root -езд, which is related to ездить (to ride). Подъехать is really “to drive or ride up to something.”

Через пять минут мы подъехали к жилому пятиэтажному дому. (Five minutes later[Елена Самойлова. «Любого мента поколотить могу!» // «Коммерсантъ-Власть», 2002]

So подъезд was traditionally a road leading to something, what we may call an “access” in English.

Для инвалидов с нарушением функций опорно-двигательного аппарата работодателям следует предусмотреть беспрепятственный подъезд к рабочему месту. (Employers should provide unimpeded workplace access for disabled people with mobility impairments.) [Мария Шаталова. Инвалидам выдадут сертификаты для устройства на работу // Известия, 2014.04.17]

It has also come to mean an entrance to a building or, specifically, the shared spaces used by all residents of a high-rise (non-rented) apartment building who share the same entrance. It follows from this definition that a подъезд comprises the front porch, the lobby, the stairwell, and landings and not only the entrance proper.

Оказалось, что он жил в том подъезде. (Literally, “It turned out that he lived in that подъезд.”) [Светлана Ткачева. День влюбленных… (2003) // «100% здоровья», 2003.01.15]

Все подъезды в этом доме ― со двора, квартиру он нашёл быстро. (All entrances in this building face the courtyard; it didn’t take him long to find the apartment.) [Анатолий Азольский. Лопушок // «Новый Мир», 1998]

Двор

Двор is a yard or a courtyard. However, unlike communities consisting of single-family homes, Russian buildings do not have a front or back yard in the traditional sense. Most people live in tall apartment buildings, some of which may form an imaginary rectangle. The space inside that rectangle is called двор.

It does not belong to a single family and may comprise playgrounds (детская площадка), parking (стоянка), pre-schools/kindergartens (детский сад). Двор is also a place where children play with each other and older adults sit on benches and socialize at night.

Своих кукол я выносила во двор и отдавала девчонкам― они в них и играли. (I took my dolls out to the courtyard and gave them to the girls — they were the ones who played them.) [Наталья Склярова. Казаки-разбойники (2002) // «Вечерняя Москва», 2002.01.10]

Из-за отсутствия достаточного количества парковочных мест во дворах приходится парковаться вдоль дороги. (Because there were not enough parking spots in courtyards people have to park along the road.) [Татьяна Бородина, Роксана Аветисян. Для запуска трамвая парковку в центре сделают односторонней // Известия, 2014.06.30]