The iconostasis and the rood screen are entirely different in their origin, purpose and function.
In the east the iconostasis developed in the first few centuries of the Christian era as a result of positioning of the most important of the church icons (probably initially displayed on the far eastern wall of the sanctuary) in association with the templon and architrave. The templon, originally a low solid screen pierced with central doors, separated or, more correctly, demarcated the sanctuary and altar from the nave. Its closest equivalent in the western churches is the chancel or altar rail, where communion of the laity takes (took) place. In terms of liturgical theology the iconostasis, by virtue of the sacred persons and events displayed thereon, does not separate but rather unites the heavenly kingdom (the altar and holy table) beyond with the earthly kingdom before (traditionally surmounted by the image of Christ Pantocrator in the central dome of the body of the church building).
The rood screen is a medieval complex development with a completely different significance. It was indeed common in parish churches. In cathedrals and monastic churches it essentially duplicated the pulpitum – a solid screen which formed a complete barrier between the clerical or monastic enclosure of the church and the secular area or nave into which the laity was permitted to enter; the pulpitum allowed the clergy to meet with the laity through a central door or gate to deliver homilies etc; access to the ambulatories through side doors or gates allowed the laity to visit and venerate the shrines and relics commonly positioned beyond the high altar, separated architecturally and liturgically from the sanctuary and monastic choir. The nave itself in large cathedrals and monastic churches had its own altar where, presumably, the laity might receive holy communion, as well as various side chapels and side altars - this was also the case, to a greater or lesser extent, in medieval parish churches.
The rood screen developed principally after the development of the doctrine of transubstantiation at the Lateran Council of 1215; the reserved sacrament within the chancel and high altar area was to be effectively screened and kept separate from the nave area of the church which was not infrequently used for secular purposes, being most often the largest enclosed area within a village or parish. The screen was not always provided with doors or gates (the chancel, the priest’s area, had its own entrance door in the south (or north) wall) and so could form a complete barrier between nave and chancel. However, unlike the iconostasis, it never became solid but remained low and allowed the laity to view the elevation of the bread and wine in the course of the mass (slots and ‘windows’ in internal church walls and pillars also exist which allowed priests celebrating at side altars to follow the mass at the high altar and to time their prayers with those of the celebrant at the main altar). At the most the rood screen itself was topped with ornamental tracery which would often connect with the rood beam above, which supported the great rood or crucifix itself. In due course, there might be associated with this upper beam a rood loft, a sort of gallery (often accessible by stairs set into the pillars) and which allowed the illumination of the crucifix and its related images by candles and lamps. In some cases the rood loft was sufficiently large that parts of the service may have been sung or chanted from that position although it is unclear how common this practice might have been.
The screen itself (about 3-4 feet high, sometimes a little more, plus the tracery above) was usually decorated with colour or gilding or ornate carving; often sacred images were applied and all this was most often provided and paid for by the wealthier members of the community. At the time of the reformation, at least in England, Wales and Scotland, the rood or crucifix was removed and the images on the screen defaced or obliterated (although some medieval work survives) as a response to ‘superstition and idolatry’; often the images were replaced with biblical texts. The screen itself remained intact (although the rood beam and loft (with very few exceptions in particularly remote areas) disappeared) and was in fact for some time a requirement of the reformed liturgy which promoted as distinctly different acts the preaching of the word to the people in the nave and the gathering of those suitably prepared at the altar or holy table within the separated area of the chancel for the celebration and reception of holy communion.
Elsewhere in Europe the removal of the rood screen seems to have occurred largely as a result of the counter reformation and as a response to the implicit requirements of the mid sixteenth century Council of Trent that the celebration of the mass should be made much more accessible to the laity.