Canon A1 camera was made from 1978 to 1985.
There are 7 screens for the Canon A1 camera. The screens are named and identified by an alphabet.
The following information can mostly be credited to page 95 of Canon's manual for the A-1, with some additional explanation where I think it is necessary.
Screen A - Microprism
It has a Matte/Fresnel field with microprism circular spot in the center of the screen. Suitable for general photography with most lenses.
Screen B - Split-Image
It has Matte/Fresnel field with split-image rangefinder spot in center of screen. Ideal for focusing at full aperture with fast lenses. Unsuitable for photo-macrography and for use with lenses having small maximum apertures or requiring stopped-down metering, because half of the rangefinder darkens.
Screen C - All Matte
Overall Matte/Fresnel field. Especially recommended for macro and telephoto photography, this screen enables the entire field of view to be seen
without distraction. The lens is in focus when the subject can be clearly seen.
Screen D - Matte/Section ("section" is old fashioned term by Canon for Grid Lines).
This screen is similar to the C screen but with horizontal and vertical reference lines. Recommended for architectural photography and copy work in which accurate image placement is essential. When using this screen, (if you are using the camera's built in exposure meter) set the exposure compensation dial to +1/3 step higher.
If you are using a separate hand held exposure meter, then there is no need to set the exposure compensation, when using this screen.
Screen E - SpIit-image/Microprism
This is the screen that is default standard screen fitted on the A-l when it is sold.
The E screen is composed of three different focusing aids: a microprism ring and a split-image rangefinder in the central area, and a surrounding matte screen. The split-image rangefinder tells you that the image is "in focus" when the image, which is divided horizontally when out of focus, merges to become one complete image. The microprism rangefinder presents a clear, steady image when in focus but a broken, shimmering image when not accurately in focus. When your desired subject is sharp, you know that the focus is correctly set. You can focus with any of these three focusing aids as you like depending on the subject and your preference.
Screen G - Microprism for Slow Lenses
This screen is similar to Focusing Screen A, but the angle of the microprisms contained within the circular centre spot is designed to work especially well with lenses having maximum apertures of f/3.5 — 5.6. Most suitable for telephoto lenses.
This screen is UNSUITABLE for larger aperture (faster lenses like F1.4, F1.8, F2 or 2.8) lenses because of focusing inaccuracy when used with them.
Screen I - Double Cross-hair Reticle
This is a highly specialised screen. It has Matte/Fresnel field with 5mm clear center circular spot containing double cross-hair reticle. While focusing, move your eye left to right. If cross-hairs stay in the same position on the subject, then the subject is in focus. Recommended for photomicrography, astrophotography, or other applications requiring high magnifications.
[Your Question] "are these 2 screens using different methods of focusing?"
[Answer] Yes, two different methods. In the matt screen you can focus using the entire surface of the screen.
In the split image screen, you focus by aligning the subject using the split image.
[Your Question] "or is my friend's screen is the same as mine just without the split image?"
[Answer] Your friend's screen is screen C. According to your description, your screen is probably screen B.
If so, then your statement is correct.
But if your screen is actually the default standard screen E, then your statement is incorrect; because there is a microprism ring around the split image.
