Just putting my "expectations" out there.
Birthday drinks - Get text about birthday person being at X pub/bar on X date for a drink for their birthday. Buy own drinks, no food on, the gift is the drink that you buy for the birthday person (this is what, imo, the OP is doing).
Birthday Party - Get text/invite to attend X venue on X date for a party. Venue decorated, posh frocks all round. Buy own drinks, will be a buffet, music and dancing. Take gift if close friends, buy them a drink if not.
Birthday Party at home - Text etc, take bottle as gift to hosts, food on but probably BBQ or pot of chilli or similar. Music, dancing. Take gift. And hosts will be left with more booze than they started with due to stocking up for party and guests drinking less than they bought.
Birthday drinks at home - rare ime but happens, basically same as above but with maybe a few bags of crisps and fewer gifts.
ETa
Forgot to say that the key is in the wording of the invite. If the word "Party" is involved, then yes there is a certain expectation of hosting. However "We are getting together for a few drinks for X's birthday if you would like to come" says that they will be there anyway and you are welcome if you would like to join them for a drink.