Is pumping considered "breastfeeding"?

I started off breastfeeding but transitioned to full time pumping mainly so my husband + in-laws could help out with feeds.

It seems like there's a hierarchy of breastfeeding being 'noble' and 'healthiest', and formula being a modern and convenient choice; but pumping is in this strange in-between. People talk about it being so difficult, but not quite as 'healthy' as EBF.

Am I depriving baby of health benefits by pumping? Do we think pumping counts as breastfeeding since the milk is coming from the same place?

-an anxious and confused mom