Simple answer. Both! Let me explain.
Semantics is a rather complex topic to get into, however, link text on a page is still viewed as content and therefore contains semantic value in determining what content is about. It simply melds into the content.
The link text is also viewed as content that describes the target page. It is weighted heavily in semantic value for the target page.
The best goal for link text is that it makes sense and has value within the content and yet also fully describes the target page which is why links within content are so powerful. SEOs often recommend using just a few keywords in the link text, however, since the beginning of Google, this has always been counter productive. The best tactic is to link a portion of the content within a sentence that describes the target page. There is little or no semantic value for just two or three keywords words as SEOs recommend. Semantics cannot make much use of just a few words. However, a full sentence or major portion of a sentence can have semantic value to fully understand the target page.
Also consider semantics between pages. A content page with a link will be related to the target page of that link even if they are not related. Hence the logic of making sure that linked pages are related by topic. In this case, the content block where the link resides, being defined as paragraphs and blocks of content between header tags, should normally relate to the link target page. In this way, a link for blue widgets in a paragraph about manufacturing widgets would indeed pass-on the value of the term manufacturing though with less weight than the link text. In this case, blue widgets would have significantly more value since in the search world links are a primary source of valuable semantic clues.
Why is this important?
Since day one of Google, links and title tags held special value in that the quality and accuracy of the match using these values proved to be a few percentage points greater than a match against the content itself. This cannot always be true if the link or title tag is short. Hence why Google does not like short title tags. Google does not match search directly against the link tag itself as it exists on a page. This is because Google believes that the link values the target page. However, Google does take into account the link text of the links pointing to any page in matching search intent. Hence why it is important.
Clear as mud?