The sides of the drawers indicates pine. The grain that is visible behind the wash/paint = pine. If the facing on the drawers are pine, then the entire thing is probably pine.

Pine doesn't like to take stain...but it can be done with HUGE amounts of PREP (prep assumes there is not PAINT on the surface like your piece) and plenty of first hand knowledge as to how to get pine to accept stain.

The type of stains that pine likes to take = very, very, very dark. So dark it almost looks painted. The other "stain" option is a "natural" colour such as a traditional finish. You will get a strong gold/orange colour with a natural finish. That's the easiest thing to get pine to accept. But then you have to LOVE the orange/gold/reds of pine to be happy with it.

Paint is what pine does best. Sadly the person who painted out this piece didn't get the job done. Normally when you paint, you want FULL coverage of the grain. If you "wash" the wood with a thinned down paint, you are hoping to see LOTS of grain. It looks like the previous owner failed on BOTH of these attempts.

So...you can go ahead and paint. That will require a good sanding, 2 coats of really good primer and then 2 coats of a cabinet grade paint. The cabinet grade paint may or may not need a coat of polyurethane afterwards. This is one of the easiest options.

If you choose to strip all the paint, you should do it by sanding (please do not use chemically strippers...they prevent future finishes from grabbing). Once ALL of the paint is gone (and I mean ALL OF IT) you can then go ahead and either stain (very tough to do) or simply finish in a natural urethane/polyurethane.

Good luck.