No, there are no terms lists that I know of in the basic version. Comparison of the two are here: http://endnote.com/product-details/basic and near the bottom of the comparison list, “Journal Abbreviation recognition & standardization” is only present in the desktop version.
You may need to ask customer service or tech support at www.endnote.com/support – but I don’t think the “online” capabilities change if you have or do not have the desktop version. But since the libraries are synced - you can format with either the online library or the desktop library and combined with the traveling library, means you can use the desktop functionalities with a paper formated with the online libraries. But others here might comment with more experience in the online functionalities. I don’t use that work flow.