Definitions straddle a line between things that clearly require attribution and things that are "common knowledge" and do not require attribution. For example, if I write on my own that:
influenza is a viral disease of the respiratory system that causes fever, aches, and other symptoms
then I need not attribute any source, because this is common knowledge. On the other hand, if I copy verbatim the Merriam-Webster definition:
a common illness that is caused by a virus and that causes fever, weakness, severe aches and pains, and breathing problems
then even though it's almost identical, I need to attribute the source because they aren't my own words. For such simple and widely accepted information, that attribution might not need a formal reference or even quotes, e.g.,
The Merriam-Webster dictionary defines influenza as a common illness that is caused by a virus and that causes fever, weakness, severe aches and pains, and breathing problems.
Quotes would be better, but the attribution is still clear, so it's a minor problem at worst.
Now, how does this apply to the situations that you have described?
- First and foremost, if the definitions are being taken from standard references, the link to standard references is valuable for students to know, so from a pedagogical point of view they should be included even if it weren't strictly necessary.
- If a large number of definitions are being presented specifically as the professor's own work, when they are not, then it is clearly a case of plagiarism (albeit a particularly banal and pointless one).
- If, on the other hand, they are being presented more generally as "information about the subject", then it is more of a grey area. They should be attributed, but informal material like course notes is often treated quite sloppily in practice, and it is likely to be perceived as a shortcoming to be corrected rather than a serious issue of plagiarism.