To operate these you need to squeeze a handle, or sometimes compress a chamber to make manual suction and extract milk.
Double Electric
These have an electric motor that create suction to extract breast milk. They can pump both breasts at the same.
Portable/wearable
Also an electric motor, but much more discreet and can be worn under your clothes in a pumping bra.
Hospital grade
These are the strongest, most efficient, electric, multi-use rental pumps typically utilized by those with infants in the NICU for prematurity or other medical conditions preventing effective breastfeeding.
How do I pick a pump?
Take into account a few factors before choosing a pump:
Suction strength - some pumps have higher suction which make pumping more effective. But others (typically those who have a fast flow and sensitive nipples) find a lower suction more comfortable.
Portability - if you will be consistently pumping at an office or during a commute, then a pump with a battery pack that you can use in different locations would be best. Some are smaller than others too, which help if you're in a small living/working space.
Connectivity - if you like to track all of your output and pumping sessions, then pick one that connects to your phone via bluetooth.
Customization - many pumps have settings with adjustable vacuum and cycles to help customize to your flow and comfort level. Others have less bells and whistles and are known for being durable and under warranty.
Discretion - this goes along with portability. If you'd like something even more convenient besides just battery controlled, you can get small pumps that you wear in your bra so you can pump very discreetly. These often tend to be quieter as well.
Price - breast pumps can be pricey, but many are covered partially or in full by insurance providers! Remember you can use FSA/HSA funds (if applicable) for things like milk storage bags, pumping bras, etc. *Check your individual plans
Examples of pumps
Manual pumps: If you will be at home with your baby, do not plan on returning to work, or are not planning on offering bottles frequently then a simple hand pump may be all you need.
These are affordable and effective. Something like this- Medela Hand Pump
The HaaKaa is a soft silicone "pump" that gently withdraws milk from the breast without continuous manual squeezing.
Double electric: If you will be returning to work or are planning to pump and offer a bottle at some point, then a double electric pump is likely the best choice.
These cost a bit more, but some insurance companies will cover part or all of the cost.
Tend to be more expensive, and not always covered by insurance
Elvie makes another wearable pump called the Elvie Stride which is more affordable. The Elvie Stride does have some tubing attached, but is still very discreet
Hospital grade: These pumps are typically RENTED and not purchased, as they are very expensive and not often required considering the double electric pumps on the market are very effective and work well for the majority of breastfeeding parents.
If you have a premature infant, or have been told by an IBCLC to get a hospital grade pump, then here are a few links to places that will rent these types of pumps