As others have already correctly said, "marshrutka" is a colloquial version of "marshrutnoe taksi", that is, "routed taxi". This concept emerged in late 1930s when Moscow started operating a few ZiS-101 limousines between the city center and VSKhV (later VDNKh/VVTs, now again VDNKh), so that every proletarian could enjoy the luxury of a government limousine for an affordable price.
Russian legislation does not use this term since around 2007. Even before the legal concept of routed taxi was abandoned, there was a great variance in models of operation between cities. In fact, in many places real-world marshrutkas didn't comply with the regulations, and that was partially why bus legislation was revised to drop the term.
So, in modern parlance, the word "marshrutka" is a legacy colloquial term that means some kind of bus or minibus service, but the particulars are still variable.
For example, in Nizhniy Novgorod, marshrutkas are most often small or medium PAZ buses allowing for standing passengers and stopping at designated bus stops at request (passengers at stops wave hands, passengers alighting push a button above doors). In many other cities, marshrutkas are GAZelle or similar minibuses, where all passengers are expected to be seated (which is often not true) and can board and alight not only at designated bus stops but also between them.
In comparison to what is called "avtobus" (bus), marshrutkas have some of the following properties:
- Marshrutkas are privately-owned and operated.
- Avtobuses are government or municipality-owned and operated.
- Marshrutkas are operated by smaller class of buses than avtobuses.
- Marshrutkas only accommodate seated passengers.
- Marshrutkas only normally stop on request, sometimes given by voice, sometimes by pressing a button.
- Avtobuses normally always stop at designated stops.
- Marshrutkas can stop everywhere where driving rules permit, not only at designated stops.
- Marshrutkas operate without a published/imposed schedule; in particular, when departing from a major passenger-generating point such as a metro station or a mall, they may start on full occupancy.
- Avtobuses operate on a schedule.
- Marshrutkas are not integrated into a city-wide fare scheme.
- Avtobuses are integrated into a city-wide fare scheme.
- Marshrutkas are not allowing free rides (or reduced fares) for privileged social groups such as pensioners.
- Avtobuses allow free rides for privileged social groups such as pensioners (usually subject to limitations).
For each of these properties, there is at least one city where this property is true and at least one city where it is untrue. Note that these differences are most often not formally codified and constitute part of the culture of a given city.
It is a Soviet tradition which is still in force in Russia that different modes of transportation have independent numbering schemes. For example, a single street may be serviced simultaneously by avtobus 2, trolleybus 2, tram 2 and marshrutka 2, each service having its own route. When Russian legislation abandoned the term "marshrutka", existing lines had to be somehow distinguished between. In Nizhniy Novgorod, this was achieved by keeping the traditional prefix "T-" for marshrutkas and adding "A-" before avtobus bus lines. In other cities this might work differently.