Also, from my own experience, my little girl (now 11 months) still sometimes gags. She bows her head down, opens her mouth, closes her eyes and her face goes slightly pink to red - to describe it better she looks like she might vomit at any second, then the piece that is bothering her moves forward in her mouth. Usually she then continues chewing it or just spits it out.
I usually count, to 5 if she isn't making any sounds, to 10 when she makes sounds while doing this and if I see her struggling I will get up and pat her firmly (not violently!) on her back. In the 6 months I have been doing this exclusively (not the patting on her back bit but the BLW bit

) I've had to pat her twice - once because she ate a hard simba chip and once while sucking on an otee but both times I actually overreacted because looking back, by the time I patted her back the piece of food was almost out already.
But not once was she actually choking. These are the true signs of choking as described in Wikipedia:
# The person cannot speak or cry out, or has great difficulty and limited ability to do so.
# Breathing, if possible, is labored, producing gasping or wheezing.
# The person has a violent and largely involuntary cough, gurgle, or vomiting noise, though more serious choking victims will have a limited (if any) ability to produce these symptoms since they require at least some air movement.
# The person desperately clutches his or her throat or mouth, or attempts to induce vomiting by putting their fingers down their throat.
# If breathing is not restored, the person's face turns blue (cyanosis) from lack of oxygen.
# The person does any or all of the above, and if breathing is not restored, then becomes unconscious