Issues with Forecast Formula v Computerised Trend

Examples, examples... OK, just one example.
Because it normally works just fine

There is probably very little we can do without a better, more detailed description, or, better yet, an example of your spreadsheet file.

2 Things I would check if I could:

The FORECAST() function regresses against a basic straight line equation y=mx+b. Chart trendlines can be based on this or other equation types. Make sure your trendline and regression function are using the same equation form.

Input data to the regression: Sometimes, chart trendline algorithms and the spreadsheet functions get different input values to the regression (especially for the "known_x values" parameter). Make sure that the input values to each regression are the same.

Updated example showing both trend line and forecast function.
To add one more potential source of errorr - carefully check if x and y ranges are not mismatched

I hope you can see this attachment, I'm having difficulties with this website!

The current trend lines you see in the charts are my formulated ones, when I add computerised trends to series 1 they are mis-matched.

Your sample file only shows the results of your "Forecast" function. I see no other trendlines in the charts or elsewhere in the spreadsheet.

I note that your input range to the FORECAST() function is restricted to the 2009 to early 2011 time frame. Perhaps this is the source of the disagreement?

I note that, if I add a trendline based on series 1 (the series restricted to rows 8:34), the resulting trendline exactly matches the FORECAST() trendline. A trendline based on series 2 (the entire data set), naturally, has a different trendline. Is this the disagreement you are talking about?

But you do the forecast just for the few first dates (in I8):

Formula:

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while your trendline is based on all data, so is equivalent to:

Formula:

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If you use formula which refers to all data, and copy it down you'll get perfect match.

Another approach is presented for team 2. I left your equation, but used excel to draw trendline for your series1 (so only first part of data, the same, you use for FORECAST.
Again - perfect fit achieved. This case for trendline I set extrapolate forward 59 units to have trendline giung further than data ends.

For both graphs, series with forecast is drwan with thick dotted line, because otherwive trendline was totally invisible (covered by forecast line).