Embroidery Library has a chart available where one enters various thread manufacturers and numbers to exchange to Madeira brand.
https://www.emblibrary.com/EL/Match.aspx
Some distributors have their own exchange list so I would recommend visiting those sites, too.

I have used google to look up different colour charts.

Used those in my early days of embroidering, but I spent too much time going from chart to chart; it felt like homework. Now I select the colors I think will be pleasing, place them on my fabric and carry them to a sunny window or my (true color) OTT light. If something looks off kilter, or distracts, I bring in a few substitutes and change them out till satisfied. Another hint you didn't ask for: when I got new kitchen counters, I carried big spools of favorite colors I was considering for an accent and looked at them on the counter in sunlight and (ugly) nighttime fluorescent lighting. Was quite surprised that what I wanted to work did not and that a cheery Christmas red was delightful! No more running to the paint store for samples...

Nope...I select my own colors...I do sometimes pay attention to the "general" color, like blue or green or pink...but I select the suggested color from my assortment of threads. Many times, I change up many of the colors for others that I like better...pink can become purple, yellow can become orange, black can become charcoal...I don't pay any attention to the brand used in the color chart, just the basic color or hue and go from there.

Hi Penny, I normally use Robison Anton and Hemingworth, but for that huge Santa quilt I made I ordered the Isacord threads which were matched to the Artist's colour suggestion. I'm so glad I did, as it turned out perfect. If I want something to match I do print out a colour chart that matches the colours suggested. Love Chris