Whether the Vlan10 and Vlan20 in the Center Router are two virtual router interfaces?

Question

I have a ISP 4321 Router in my Cisco Packet Tracer. and I added a NIM-ES2-4 module in the Router, that provides four switching ports. and now, I configured two VLANs to the two switch port of them. and now it created the two VLANs, you can see below, there are Vlan10 and Vlan11:

Router#show ip interface brief 
Interface              IP-Address      OK? Method Status                Protocol 
GigabitEthernet0/0/0   unassigned      YES unset  administratively down down 
GigabitEthernet0/0/1   unassigned      YES unset  administratively down down 
GigabitEthernet0/1/0   unassigned      YES unset  up                    up 
GigabitEthernet0/1/1   unassigned      YES unset  up                    up 
GigabitEthernet0/1/2   unassigned      YES unset  up                    down 
GigabitEthernet0/1/3   unassigned      YES unset  up                    down 
Vlan1                  unassigned      YES unset  administratively down down 
Vlan10                 10.10.10.1      YES manual up                    up 
Vlan11                 10.10.20.1      YES manual up                    up

I want to know whether the Vlan10 and Vlan11 are two virtual Router ports?

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If the Vlan10 and VLan11 are two virtual Router ports. I have configured the IP address on them, you can check the upper data. and I assigned the Vlan10 to GigabitEthernet0/1/0, the Vlan11 to GigabitEthernet0/1/1, all are access mode.

but now I cannot from 10.10.10.2 to ping 10.10.20.1:

Router>ping 10.10.20.1

Type escape sequence to abort.
Sending 5, 100-byte ICMP Echos to 10.10.20.1, timeout is 2 seconds:
.....
Success rate is 0 percent (0/5)

the Center Router(Router11)'s route is bellow:

Router#show ip route
Codes: L - local, C - connected, S - static, R - RIP, M - mobile, B - BGP
       D - EIGRP, EX - EIGRP external, O - OSPF, IA - OSPF inter area
       N1 - OSPF NSSA external type 1, N2 - OSPF NSSA external type 2
       E1 - OSPF external type 1, E2 - OSPF external type 2, E - EGP
       i - IS-IS, L1 - IS-IS level-1, L2 - IS-IS level-2, ia - IS-IS inter area
       * - candidate default, U - per-user static route, o - ODR
       P - periodic downloaded static route

Gateway of last resort is not set

     10.0.0.0/8 is variably subnetted, 4 subnets, 2 masks
C       10.10.10.0/24 is directly connected, Vlan10
L       10.10.10.1/32 is directly connected, Vlan10
C       10.10.20.0/24 is directly connected, Vlan11
L       10.10.20.1/32 is directly connected, Vlan11

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So my questions are:

1. Whether the Vlan10 and Vlan20 in the Center Router are two virtual router interfaces?
2. Why the Router 10 can not ping the Router11?

Answer 1

1. Yes, these also called switch virtual interfaces or SVI.
2. Because your Router10 don't know how to get to 10.10.20.0/24 network. Add route to Router10 configuration:

#(conf-t) ip route 10.10.20.0 255.255.255.0 10.10.10.1