Each major tool maintains its own crawler and link index. The size and freshness of that index is the single biggest differentiator. Ahrefs, Semrush, and Majestic each crawl billions of pages per day; smaller tools either license data from one of the big three or build smaller indexes.
For your own site: Google Search Console. For competitors: Ubersuggest free tier or the limited free Ahrefs/Semrush previews.
Each maintains its own index with different crawl frequency and inclusion rules. Differences of 20-50% are normal; if you see 5x differences, the smaller index is missing data.
For agencies and serious in-house teams, yes. For occasional use, the free tier of Ubersuggest or Semrush trial periods cover most needs.
Wrong question. Quality, relevance, and topical match matter far more than count. 50 great links beat 5,000 mediocre ones.