When you are replacing a site, if you keep the same information (generally) on page, even if you change all the images and all the text, but the subject of the page is the same and you are using the same url, then there is no need for a redirect.
In your example above, if the old url was
www.mysite.com/cabinets.html, you could replace all the content (refresh images and re-write the text) and not need a redirect as long as you felt the content on that page was relevant to the visitors of the old page. If you decide to change the url to
www.mysite.com/my-work/cabinets then you would need a redirect.
You only put the redirects in place after the new site is in place.
Let’s take another example, let’s say you had a page on the old site called
www.mysite.com/contact.html. You decide that in the new site that is better under an About Me section, so you have it at
www.mysite.com/about-me/contact-info. Once you replace the old site, if a search engine indexed the old page and it’s now gone, you will lose some of the page ranking associated with it. If you setup a redirect to the new page, you will transfer your ranking to the new page. Also, if anyone bookmarked the old
contact.html, they will get an error about the page not being found. With the redirect setup, they will just appear on the new page.
Redirects are only needed if the url for the same content (subject) is changed. If you keep the url, no redirect is needed. They are also important for any page urls that will not be used in the new site.
A lot of times when people redo a site, they tend to adjust things, and they often change page names and website structure, since they now have a better idea of how they want their site to be navigated. They don’t keep track of the old page names and don’t setup redirects and have issues with less organic search traffic.
Also, it was common to have a more flat structure with each page ending in
.html, usually right off the site root folder. Now it’s much more common to have each page in it’s own folder with the page named
index.html. This way the url is simpler.
www.mysite.com/contact.html/ can become
www.mysite.com/contat-me. This is usually referred to as cruft-less links.