What are the difference between the 3 different races

You'll really have to play each to see it in detail, but basically:
- TEC are driven by economy so your best strategy is to get trade stations up and working quickly and outpace the fundraising and fleet creation speed of the other two races.
- Vasari are nimble, based on mobility and speed more than the other races. Their later buildings and abilities allow them to move around much faster than the other races, as long as you survive that long. Vasari specialize in harvesting resources (metal and crystal).
- Advent have the most "magic" - psychic and psionic abilities, and they have the best propaganda/culture and strike craft abilities. They don't have a resource specialization.

It would take a Very Long Post(TM) to list all the tactical differences, but exploring other areas of this strategy forum will give you an impression.

Enjoy the game.

-- Retro

All races have most things simlar, such as each one has the same kinds of frigates, and even the same roles to their cap ships but they have different names/looks and ways of fullfilling that role. The biggest difference that becomes obvious is that it is mainly the tech trees and their differences that define the races.

TEC
Easiest to get a high credit income established, TEC are frequent users of the black market to make up for their lack of ability to resource crystal. Lots of use of trade ports is essential.
Thier ships strength is in their hulls compared to Advents strong shields.
TEC probably have the best fleets early game, able to get more ships than Vasari and established easier than advent because of their economy and the cheaper route to their LRMs than Advents Illuminators. But this also means TEC need to be aggressive early on, hurt the enemies economy and research ability as soon as they can. If games go on a long time TEC require a lot more micro management to counter Advents strong cap ships, and need to be aggressive to ensure Vasari don't get established.

Advent
Are meant to be defined by their culture spread, it's up to you discover how important this actually is in terms of use. I often use culture when i'm spreading into enemy territory to increase my spread speed, and also on certain borders I am only defending on, not attacking on however it's not that powerful an advantage.
Advent have research and abilities that make their ships shields the most powerful of all 3 races.
The main difference when using Advent for me appears to be the strength of the Capital Ships. If you are able to get some high level ships complimenting your fleet you are in an extremely strong position as Advent.

Vasari
Early game they can get their Long range frigates pretty much straight away (Kanrak Assailant) and so can begin building a powerful fleet almost as soon as they kick off. Vasari ships are more powerful than their TEC and Advent counterparts but are more costly and you can't have as many at the same time (each costs more fleet supply). Phase Missiles research also define Vasari's fleet makeup and strength mid game and later.
Vasari are great resource collectors, able to research improved metal and crystal extraction under 1 ability.
Late game which is more relavant for private multiplayer games or AI battles (as most online games don't last this long) Vasari's strength is in their amazing mobility, unlike other races they can use their phase lanes to always be within 2 or 3 jumps of any trouble.
Once you kick in Returning Armada with established phase lanes as Vasari you can just pop up your fleet supply and mop everyone else up.

I find that the races are all very similar. They all have the exact same ships and nearly the same research, except that there are minor variations within that. The Illuminator is harder to get, but stronger than the TEC LRM, for example. Basically though, you can be any race, and choose any strategy you want and it will probably work out fine. The differences are not as big as they seem...

For example, the TEC's LRM uses less fleet points than the illuminator, so you can get more of them faster. Basically it all evens out in the end, and you're just choosing races based on which captitol ship abilities you like the most (which, btw, also are basically equivalent in the end...).

They really aren't all alike in the end. They are all significantly different in various ways that affect the strategy. One of them is very good for playing on small maps and the other is good for large maps that have relatively fewer players (but you wouldn't want to play them on a small map or a map with a large number of players relative to the number of planets) while one is pretty decent on medium and large maps.

Disagree with Alexboculon. The races are quite different, particularly near end-game. The superweapons in particular demand greatly different strategies.

-- Retro