A restaurant and a mosque were targeted on Sunday night.
No-one has claimed responsibility but militant group Boko Haram has attacked Jos before, even though it is not in north-east Nigeria where the Islamists normally operate.
The blasts are the latest in a series of deadly attacks in recent days which have seen more than 200 people killed.
The attacks came shortly after the Ramadan fast was broken, with both sites full of people.
Of the 44 dead, 23 were killed at the restaurant and 21 at the mosque, Nigeria’s National Emergency Management Agency (Nema) says.
There are also 47 people being treated for injuries, but emergency officials are still gathering information, so the figures may rise.
The blast at the restaurant was caused by a bomb that had been planted, whereas the mosque was attacked by a suicide bomber and that explosion was preceded by gunfire, the BBC’s Ishaq Khalid reports.
Eyewitness Akaria Ahammed said: “When they started shooting people, people started running helter skelter for their lives.
“Unfortunately those that stood up were shot.”
Our correspondent says that many believe that the mosque’s imam, who was preaching at the time, may have been the target.
Sheikh Muhammad Sani Yahya Jingir, who survived the attack, is known for preaching against Boko Haram and has written a book, which criticises the group, called Boko Halal (Western education is permitted – Boko Haram means Western education is forbidden).
He has survived a previous assassination attempt at his home and is seen as one of the most influential clerics in Nigeria.
It is not unusual for there to be a heightened risk of jihadist attacks during the holy Muslim month of Ramadan.
Boko Haram may be trying to deepen its ties with the jihadists fighting in Iraq and Syria who had called for “a month of disasters for the infidels”.
Many of the recent attacks have been by suicide bombers – often young women.
Where the bombs are being made and where the bombers are being brainwashed is unclear but the Nigerian intelligence and security services need to do far more to stop the bloodshed.
Once again the range of targets is alarming and on this latest bloody Sunday a church and a mosque were bombed within hours of each other.
The city has in the past seen clashes between Muslim and Christian communities and some have suggested that Boko Haram is looking to exploit these fault-lines.
Sunday: Church attacked in Potiskum, in Yobe state, killing at least five.
Friday: Several suicide bombers kill large numbers in Zabarmari village, north-east Nigeria.
Thursday: Two female suicide bombers attack another village in Borno state.
Wednesday: More than 50 gunmen kill 97 people in the village of Kukawa, near Lake Chad.
Tuesday: 48 men shot dead after prayers in two villages near the town of Monguno, Borno state.
On Friday, Nigeria’s President Muhammadu Buhari described the recent attacks as “inhuman and barbaric”.
In power now for just over a month, the president was elected on the pledge to defeat Boko Haram.
He said they were “the last desperate acts of fleeing agents of terrorism”.
Boko Haram took control of a large area of north-eastern Nigeria last year and declared a caliphate – a state governed in accordance with Islamic law.
However, Nigeria’s military, backed by troops from neighbouring countries, has recaptured most of the territory.
President Buhari has called for an expanded regional force to be deployed more rapidly.