They can be similar looking but there are some fairly distinct differences in the tentacle shape, the verrucae, the overall shape, and their habits (espescially where they choose to attach and so on). The tentacles are usually longer on
M. doreensis, they tend to spiral into a corkscrew shape sometimes (hence the common names "long-tentacle anemone" and "corkscrew anemone").
Entacmaea quadricolor can have tentacles that bubble-up hence the common name "bubble tip anemone." But BTA's don't always have bubbles and the reasons for this are not well understood; suffice it to say "they may or they may not." But the "BTA" name still references back to the species name so just because it doesn't have bubbles doesn't mean it's not a BTA.
You can do some reading on the field charactistics of these species and the other Indo/Pacific hosting species over at
http://biodiversity.uno.edu/ebooks/intro.html
Fautin and Allen are generally regarded as the forefront experts on the hosting species of anemones and this link is an online version of their book "Field Guide to Anemone Fishes and Their Host Sea Anemones". The print version is more complete than the online version so if it's something you're interested in, you should find the printed version somewhere.