Is it appropriate to put master's and bachelor's theses into ORCID web page as dissertations?
Yes, this is certainly appropriate and acceptable - but probably good to make clear the level of the document to avoid confusion. (I have my MSc thesis linked from my ORCID.)

The Wikipedia article on "thesis" gives a good overview of the difference in terminology - in short, "thesis" or "dissertation" can mean either an undergraduate work or a doctoral work, depending on the context and the location, and there is no single cast-iron rule. I wouldn't read too much into ORCID's choice of terms...