An estimate is an indication of cost (cash and/or time) required to complete an activity. An estimate is not guaranteed and has the potential to change throughout the duration of the activity. Most reputable organisations would notify you before any change, and the reason(s) for that change.
A high-level estimate is provided before thorough investigations have been done. e.g. "I'll build you an extension. The last extension I build (Without going into detail) cost £15,000 - so my high-level estimate for you is £15,000."
A detailed estimate however, is more reliable and often includes a break-down of the features of the estimate. "So, although we previously quoted £15,000 as a high-level estimate for your extension, you have told me you'd like traditional roofing slates, an extra large window, under-floor heating, and a wet room. Here's a detailed estimate for £19,000."
A quote is slightly more reliable in an estimate, in that, unless you change anything significant, you're likely to pay the price quoted. So if the detailed estimate for £19,000 becomes a quote - then you're likely to pay £19,000 even if the extension building takes longer (and therefore more man-hours) to complete. If you add a requirement for another room however, that's a significant change, and you would be likely to pay more.
A fixed-price quote is an agreement that the goods/services will definitely be provided to you at the quoted price. The provider of goods/services will have investigated that, even if the most expensive of goods are provided, or the highest quality of finish is required, the price will remain the same. Usually - any potential variations in price (e.g. what type of shower is required) will have been agreed before the work starts.