If your phone shows 4G, that is the connection technology being used at that moment.
If it shows 3G later, that is the connection technology being used. It may be the same tower, or it may be a different tower. It may even be a different provider, a roaming partner if your service permits data roaming. It is the connection your phone found. It might be a connection from a more distant tower that stayed connected as you moved, so you could maybe get a faster one by re-booting, or disconnecting and reconnecting data, if your phone allows that.
If your voice technology is GSM, the phone might also show E, for Edge, which is about 2.5G (actually 3G by global standards, except that someone made 3G a trademark in the U.S. for a specific data technology).
Some phones show the provider as well. Mine does.
Sometimes they lie about the provider part, i.e. if the connection is with an AT&T U.S. roaming partner my phone still says ATT rather than identifying the local provider. But when I am somewhere I must pay for roaming, the phone shows the actual carrier: e.g. Orange, O2, T-Mobile, Vodafone, and Telekom have all popped up on my phone the past couple of years.
