"Better search" is the most common wish for a note system, and the most common way to overbuild one. There are three different retrieval layers people mean, they solve different problems, and most of us need them in a specific order.
Layer one: exact, or keyword, search
This is matching the words you type against the words in your notes. It is instant, precise, and runs anywhere with no infrastructure. When you know roughly what you wrote, it is the fastest way back to it, and it is the first thing any system should get right.
Its limit is in the name: it matches words, not meaning. If you search "pricing" but the note said "how much to charge," exact search misses it. That gap is real, but it is smaller than people assume, because you usually remember some of the actual words.
Layer two: semantic search
Semantic search finds notes by meaning rather than exact words. It works by turning your notes into vectors, numeric fingerprints of meaning, and finding the ones closest to your query. Ask "how much to charge" and it can surface the note about pricing even with no shared words. For recall, when you have forgotten the vocabulary, it is genuinely useful.
It also costs more. You need to compute and store an index of embeddings, keep it current as notes change, and either call an external service or run a model locally. That is real infrastructure for a benefit that, for a lot of personal knowledge work, exact search plus good links already covers. Semantic search is worth it, but later than most people reach for it.
Layer three: the knowledge graph
Links are a different kind of retrieval. Instead of searching, you traverse: from this note, what connects to it, and what connects to those. A graph answers "what is related to this project" in a way neither keyword nor semantic search does, because the relationships were captured deliberately when you linked things. It is how you rediscover context you were not searching for.
The order that actually works
The useful principle is to reach for the lowest layer that solves your pain. Start with exact search and links, because together they cover most of what you need with almost no cost. Add semantic search when you can point to a specific, recurring case where you know a note exists but cannot find it by words. Building the sophisticated layer first is the classic way to spend weeks on retrieval and still not enjoy using your notes.
The layers also compound. Exact search gets you to the note you remember. Links carry you from there to the ones you forgot. Semantic search catches the ones you could not phrase. A good system lets each do its job rather than forcing one to do all three.
How LocalBrain approaches it
LocalBrain keeps exact search first-class and instant, layers links and related notes on top, and gathers everything about a project into a compiled context page so the graph pays off at the moment of work. It is the low-cost, high-return combination first, with room to go deeper when a real need shows up, not before.