In common usage, a phrase is usually a group of words with some special idiomatic meaning or other significance, such as "all rights reserved", "economical with the truth", "kick the bucket", and the like.
It does not have to have any special meaning or significance, or even exist anywhere outside of the sentence being analyzed, but it must function there as a complete grammatical unit.
For example, in the sentence Yesterday I saw an orange bird with a white neck, the words an orange bird with a white neck form a noun phrase, or a determiner phrase in some theories, which functions as the object of the sentence.
The node labels in the two trees mark the syntactic category of the different constituents, or word elements, of the sentence.
For example, in order to explain certain syntactic patterns which correlate with the speech act a sentence performs, some researchers have posited force phrases (ForceP), whose heads are not pronounced in many languages including English.
Similarly, many frameworks assume that covert determiners are present in bare noun phrases such as proper names.
Another type is the inflectional phrase, where (for example) a finite verb phrase is taken to be the complement of a functional, possibly covert head (denoted INFL) which is supposed to encode the requirements for the verb to inflect – for agreement with its subject (which is the specifier of INFL), for tense and aspect, etc.
The split between these views persists due to conflicting results from the standard empirical diagnostics of phrasehood such as constituency tests.