3 Seasons versus 4 Seasons! - There's nothing laid down defining what is a 3 and what is a 4 season tent, its up to the manufacturer to give the rating.
4 Season tents tend to be made from heavier fabrics, with higher waterproof ratings than 3 season tents, especially on the grounsheet fabric and will have additional stictching on stress points and additional guylines for stability.
But for most uses and most conditions a 3 Season tent will do the job, consider a 4 Season tent if you will be camping in Winter conditions - or if you are going away for weeks or months and you need a particularly robust tent.
Structure; Geodesic versus Tunnel, Teepee and Trekking Pole tents - A Geodesic tent will have poles that bend and intersect with the other poles in the structure - this makes the combined unit of poles and tents very strong, but the price of this strength is additional weight.
Tunnel tents have a hoop at either end and sometimes in the middle. They are not as stable as Geodesic designs but can be mae quite stable using additional guylines. Tunnel tents tend to be lightweight considering the internal space that they provide.
Teepee-style tents have a single pole in the centre and create a pyramid shaped tent. This is suprisingly wind resistant and provides a lot of headroom/internal space for a given weight.
Another way of saving weight is to buy a tent that uses trekking poles as its frame - if you use trekking poles anyway there is a great saving with this type of tent.
Mesh Inner tent versus Fabric Inner tent - Tents with an inner tent made with mesh walls are cooler than those made with fabric walls - so they are more suited to camping in warm weather. When the wind blows hard it can get under the flysheet and breeze through the inner tent. Most of these tents have deep bathtub groundsheets such that when you are lying down the wind does not disurb you.
Inner tents with fabric walls keep the wind out but they also feel more closed in, they don't feel as spacious as Mesh inner tents. Fabric inners are also warmer - it is thought that they add up to 5C to the temperature inside the tent. This makes them well suited to winter/4 season use.
Many tents have a mix of fabric and mesh so you can get the best of both worlds.
Single Skin versus Two Skin - Two skin tents were designed to combat condensation, which forms on the inside of a tent as water droplets. These can run down the inside of the tent and form a pool on the groundsheet - not ideal.
The way a two skin tent works is that water vapour passes through the inner tent and the condensation form on the inside of the flysheet - not the inside of the tent. This means that it runs down the flysheet and harmlessly onto the ground.
When condensation occurs on single skin tents it can only form on the inside of the tent itself - if you have a sewn in groundsheet the condensation will 'pool' on the groundsheet. This is not necessarily a disaster as it can easily be mopped up with a cloth - but many people don't like it.
Single skin tents can obviously be made lighter or can be more spacious, so if you don't mind condensation now and again you can save a lot of weight by taking a single skin.
Also, on any given trip, condensation will not necessarily be a problem every night - depending on conditions there is often no condensation at all.