I believe (but I may be wrong) that Dendrobium phalaenopsis and Dendrobium bigibum are the same thing. I think one is the name used in America and Europe and the other is the name used in Australia and that side of the world.
Having said that your first one may well be a hybrid as many Dendrobiums are referred to as phalaenopsis type when they are hybrids with a high proportion of phalaenopsis in it.
Just a quick note on the naming of these. The bigibum and the phalaenopsis should have a lower case first letter because they are the names of species. Hybrid names start with a capital as does the genus name (Dendrobium in this case). This helps to tell the difference between Phalaenopsis the genus and phalaenopsis the species of Dendrobium. It might sound picky but really helps people be clear what you are talking about.
Anyway, after all that, it sounds like your care is fine. I look after mine in a very similar way to a Phal. Not all Dendrobiums need the same care but these should be fine carred for like a Phal. They need higher light to bloom again though. If you can I would advise moving it to a west window, if you move it now in the winter it will have time to aclimatise to the brighter light before the really hot sun in the summer. I had to put mine outside in direct sun last year before I could get it to bloom.
These don't need a winter rest, although you may want to water slightly less in the winter. Try not to water on a set schedule (for both this and the Phals) rather try and water when they need it. I find that like Phals they can dry slightly before watering and mine seem to need it arround the same time as the Phals.