Backpacking waterproofs will be at the heavier end - they need to be durable because of the hip belt and shoulder straps so will be made of heavier fabrics. Choose a jacket at least 400g and it will be three layer fabric as this is more durable than 2.5 layer. Choose a high waterproof rating because rucksack straps press onto the fabric forcing water through. Hydrostatic Head of 20,000 to 30,000 is required.
Hip pockets will be unusable when a rucksack is being carried. Pockets add weight and compromise breathability - but when backpacking they can be useful, so chose chest pockets but not waist pockets.A wired peak on the hood is also pretty much a necessity and if you can get a hood that moves when you move your head all the better.
Typical of this category is Mountain Marathons, you will be carrying a pack but it will be quite light and may not have a hipbelt. A waterproof jacket will be the 'lightest in class' so will probably be made from a 2.5 layer fabric.
It will still have a full range of features but the design of these features is likely to be simpler. You will find it probably has elasticated cuffs and hem, a simple hood with a foam peak rather than a wired one. Pockets will be limited. The fit of this category of jacket is often called 'Athletic' - with this type of fit the jacket fits closely to the body and you wouldn't be expected to be wearing much underneath, a single baselayer perhaps.
A waterproof jacket for running will share a range of features with the Fast and Lite category - it will be an athletic fit because a runner will not be wearing much underneath, it will be very lightweight so as not to slow the runner down.
Breathability will be of paramount importance so look closely at the breathability ratings of the various jackets - this is measured in MVTR or Moisture Vapour Transmission Rate, the higher this value the better the breathability. Remember pockets compromise breathability because they introduce more layers of fabric, running waterproofs have minimal pockets anyway, and those that are present should ideally be lined with mesh.
Walking is a more general category so there will be a wider range of options depending on your preferences. Weight won't be so critical so a walking jacket will have a more comprehensive set of features, as a minimum you want a well-designed adjustable hood, pockets where you want them and an internal flap on the zip.
If you want a lightweight waterproof then you will probably be looking as 2.5 layer fabrics, which aren't as durable as three layer. Generally speaking the heavier the jacket the more durable the fabric will be. In this category you might want to consider pit zips - these are zippered vents under the arms which help a lot with breathability.
Winter conditions demand a lot from a waterproof jacket and suitable ones will weigh at least 500grams, and upwards. When the hail gets blown around in the Cairngorms you need a jacket that acts like armour - fending them off. Heavier fabric will do this easily.
You definitely need a comprehensive hood - it needs to move with your head and cinch tightly round your face so that it keeps spindrift out. Similarly the cuffs need to be reliably tight. As you will probably be carrying a rucksack, possibly a heavy one, look for reinforcements around the hips and on the shoulders. Its a good idea to have a comprehensive range of pockets - lined with fabric, not mesh. Pockets help you stay organised with headwear and gloves.