Ask your neighbor. The difference may be the type of grass or perhaps their routine for lawn care...fertilizing, aerating etc.

Thanks! Yes, i agree. The neighbor doesn’t know the type of grass she has . That’s why I’m asking if I can take it to a nursery or something to figure out what I should have

Very few nurseries specialize in turf grasses to my knowledge so you may not find your answers there. And to be honest, most turf grasses look pretty similar anyway. Also, your location will determine what types of grasses will do best for you and are common to your area. If you live in the northern tier of the country, your lawn could very well be a blend of several different types of grasses, which adds to the complexity of an identification....and the reason the sodded portion looks so different. Sod is usually just a single grass type, not a blend.

Where you live geographically also has a bearing on when is the best time to seed or overseed. In almost all cases, spring is not ideal as the grass does not have sufficient time to establish before being hit by the heat of the summer. Late summer or early fall is generally the recommended time frame.

Come back and let us know regionally where you live and then hopefully we cam be more helpful.

Making the assumption that the photo is taken recently - since the trees are not green, I'm going to guess you live in the far north. As gardengal mentioned, you likely have a blend of grasses including fescue, rye, and Kentucky bluegrass. Fescue and rye normally remains green all winter. KBG usually become brown in the winter. If you would like to influence the nature of greenness according to those guidelines, you could wait until late summer to overseed with fescue or one of the others.

For now you have what you have. What is your goal? If you're worried about it not being green, the biggest influence on greening is fertilizer. Secondary to that is mowing height. Do you want the greenest lawn on the block? Do you just want uniform greenness? Do you just want something green which keeps the mud out of the house?

When were the last two times you fertilized, and what did you use?

What is your watering routine? How often and for how long?

What is your mowing schedule? Generally weekly mowing is recommended, and I always recommend mowing at the mower's highest setting to obtain the most dense and green of lawns. There are exceptions, but yours does not appear to be one of them.

Have you used any insecticides, herbicides, or fungicides in the past year? If so, what and when?