Wifi and bluetooth speakers both have their pro's and cons, WIFI is generally better, as the quality of audio able to be transmitted can easily be CD quality or hi-res, however you would obviously need a wifi network in your home, that connects to the internet, to be able to use these, they also generally are able to link with other WIFI speakers of the same brand. Bluetooth speakers do not require you to have a home wifi network, and just make a 1 to 1 connection with a phone or tablet, some newer bluetooth versions are allowing multi point connection, but these will generally be fairly limited in their range, whereas wifi speakers are only limited by the quality and range of your wifi.

A WIFI speaker is one that is able to be connected to your home/office WIFI network, these are generally a "powered speaker" so they have built-in amplification to drive them, some examples are Formation Duos, Formation flex, bluesound pulse, Devialet Phantom, sonos Five.

WIFI speakers do not generally have "lag" per se, if you have a home fitted out with say, sonos or bluesound speakers throughout, grouping them altogether should give you a sound that is in sync with each other. The only time that Lag might be present, is when running a physical source (ie CD player/TV) to a WIFI speaker/amp and then trying to group that with other WIFI speakers around the house, this is because it has to process that analog audio first into a digital signal, before sending it out over WIFI to the other speakers.