There are some important differences between those two type of files.

BITMAP files:               for example:    *.gif, *.bmp, *.jpg, *.tif
A bitmap files is a file in which is a picture which consists of many pixels of a certain color. When you zoom in in this drawing, you will see that lines which are not exactly straight, contains steps. The more you zoom in, the bigger these steps are. These type of files is not possible to cut directly, because it contains no real lines. A plotter needs lines to cut. Some of the bitmap files are possible to vectorise (see below) after which they can be cut. Most of the bitmap files are impossible to cut, because when we cut we want to use vinyl to reproduce the picture. When the picture has many colors, we should use even as many colors of vinyl to reproduce this picture, or create a drawing with less colors which looks like this picture.
You can imagine that it is not very simple to create a drawing like this.

So, Bitmap files are not easy to plot.

VECTOR files:           for example:    *.EPS, *.AI, *.dah, *.dc2, *.CDR, *.drw
A vector file contains a drawing which is made of contours of vector lines, mostly with a fillcolor per contour. Those vector lines can be enlarged as big as you want, while they stay smooth. Those lines can be cut on a plotter, because they are contours. If we use vinyl with the color of the fillcolor, we can reproduce the drawing.  
Many programs can create vector files, but realize that many of those programs also can include bitmaps in their vector files. A file from such a program can contain vectors AND bitmaps. For cutting, we can not handle the bitmap part.

TEXT in vector files: 
Often there is text in a file. This text is made with a certain FONT, and has certain characters which forms the text. There are two ways of how text could be in the file:
1 The file contains the lines to draw all the characters (text is in curves) In this way it is hard to modify the text, but the text has exactly the size and length as it was meant to have by the designer.
2 The file contains the characters of the text, and the name of the FONT to use with this text. In this way the file is much smaller, and the text can be edited very easy. Only there are some  problems: first,  the computer which receives this file, must have this FONT in his system. Second problem, specially for SignMakers, this font should be EXACTLY the same as the font what the designer used. Even when the name of the font is the same, each manufacturer of the font could have a slight difference, so that fe. the length of the text could be a little different as was meant by the designer. Specially in a logo, the length could be critical because the text could be meant to fit exactly in a box. When this text is a little longer, the text could be longer than the box where it should fit in.

If you want to exchange files from any program, you must use a generic exchange format, such as EPS (Encapsulated Postscript) or AI (Adobe Illustrator format), or (older) DXF.

If your program cannot do this, you could use HPGL, but in HPGL all curves are converted to small line pieces. This gives not a very good result.

If you need to cut a file from Corel or Illustrator, export the file in AI or EPS format. If text is critical, convert all texts to curves before exporting (see above).(If you import in DahediSign on the same computer, you could export text as fonts, because DahediSign uses the same fonts)
If your program has more options with exporting, try to use the most simple way of EPS export. (for cutting we need only the vector lines. We do not need complex color patterns etc.) 
When the file is exported, import it in DahediSign. Now you will see the cutting lines.
Probably you will need to resize it into the real cutting size, and/or combine it with other files or texts. After this you can send it to the plotter.

NB. Adobe Photoshop can create EPS files, but it will contain NO vectors, only bitmaps, so it is not possible to cut Photoshop files.

NB. Adobe Illustrator version higher than version 8, uses an own binary format for their .AI files, so files from Illustrator higher than 8, should be exported as EPS, or AI of a lower version than 9.

Mostly you need to edit some details, because mostly the bitmap is not detailed enough to have all sizes accurate. 

If you have a bitmap, import it in DahediSign, choose BITMAP >> Vectorise, and cut the result. 

You can only see what it does when you cut the demo picture which comes with the demo version. Import the PixelplotDemo.GIF file and see what it does.